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108-870: Tikhonov (Russian: Ти́хонов ; masculine), sometimes spelled as Tychonoff , or Tikhonova ( Ти́хонова ; feminine) is a Russian surname that is derived from the male given name Tikhon , the Russian form of the Greek name Τύχων (Latin form: Tycho ), and literally means Tikhon's . It may refer to: Alexander Tikhonov (born 1947), Russian biathlete Alexei Tikhonov , Russian figure skater Andrey Tikhonov (footballer) , Russian football player and coach Andrey Nikolayevich Tikhonov , Russian mathematician Ivan Tikhonov , Russian-born Azerbaijani gymnast Konstantin Tikhonov  [ ru ] , Soviet army officer and Hero of

216-814: A Wiener–Kolmogorov (Kriging) filter. Following Hoerl, it is known in the statistical literature as ridge regression, named after ridge analysis ("ridge" refers to the path from the constrained maximum). Suppose that for a known real matrix A {\displaystyle A} and vector b {\displaystyle \mathbf {b} } , we wish to find a vector x {\displaystyle \mathbf {x} } such that A x = b , {\displaystyle A\mathbf {x} =\mathbf {b} ,} where x {\displaystyle \mathbf {x} } and b {\displaystyle \mathbf {b} } may be of different sizes and A {\displaystyle A} may be non-square. The standard approach

324-619: A constitutional referendum on whether to adopt Russian as a second official language. According to the Central Election Commission, 74.8% voted against, 24.9% voted for and the voter turnout was 71.1%. Starting in 2019, instruction in Russian will be gradually discontinued in private colleges and universities in Latvia, and in general instruction in Latvian public high schools. On 29 September 2022, Saeima passed in

432-519: A new education law which requires all schools to teach at least partially in Ukrainian, with provisions while allow indigenous languages and languages of national minorities to be used alongside the national language. The law faced criticism from officials in Russia and Hungary. The 2019 Law of Ukraine "On protecting the functioning of the Ukrainian language as the state language" gives priority to

540-537: A Tikhonov regularization in the original infinite-dimensional context. In the above we can interpret A {\displaystyle A} as a compact operator on Hilbert spaces , and x {\displaystyle x} and b {\displaystyle b} as elements in the domain and range of A {\displaystyle A} . The operator A ∗ A + Γ T Γ {\displaystyle A^{*}A+\Gamma ^{\mathsf {T}}\Gamma }

648-533: A constant term, x T ( A + Q ) x − 2 x T ( b + Q x 0 ) . {\displaystyle \mathbf {x} ^{\mathsf {T}}\left(A+Q\right)\mathbf {x} -2\mathbf {x} ^{\mathsf {T}}\left(\mathbf {b} +Q\mathbf {x} _{0}\right).} This minimization problem has an optimal solution x ∗ {\displaystyle \mathbf {x} ^{*}} which can be written explicitly using

756-642: A covariance matrix C M {\displaystyle C_{M}} representing the a priori uncertainties on the model parameters, and a covariance matrix C D {\displaystyle C_{D}} representing the uncertainties on the observed parameters. In the special case when these two matrices are diagonal and isotropic, C M = σ M 2 I {\displaystyle C_{M}=\sigma _{M}^{2}I} and C D = σ D 2 I {\displaystyle C_{D}=\sigma _{D}^{2}I} , and, in this case,

864-437: A formula with V standing for the nucleus (vowel) and C for each consonant, the maximal structure can be described as follows: (C)(C)(C)(C)V(C)(C)(C)(C) Tikhonov regularization The theory was first introduced by Hoerl and Kennard in 1970 in their Technometrics papers "Ridge regressions: biased estimation of nonorthogonal problems" and "Ridge regressions: applications in nonorthogonal problems". Ridge regression

972-484: A language that "belongs to the European cultural space". The financing of Russian-language content by the state will cease, which the concept says create a "unified information space". However, one inevitable consequence would be the closure of public media broadcasts in Russian on LTV and Latvian Radio, as well as the closure of LSM's Russian-language service. In Lithuania , Russian has no official or legal status, but

1080-588: A lesser extent the languages to the south and the east: Uralic , Turkic , Persian , Arabic , and Hebrew . According to the Defense Language Institute in Monterey, California , Russian is classified as a level III language in terms of learning difficulty for native English speakers, requiring approximately 1,100 hours of immersion instruction to achieve intermediate fluency. Feudal divisions and conflicts created obstacles between

1188-622: A minority language under the Framework Convention for the Protection of National Minorities . 30% of the population was fluent in Russian in 2006, and 2% used it as the main language with family, friends, or at work. In Azerbaijan , Russian has no official status, but is a lingua franca of the country. 26% of the population was fluent in Russian in 2006, and 5% used it as the main language with family, friends, or at work. In Georgia , Russian has no official status, but it

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1296-541: A particular solution with desirable properties, a regularization term can be included in this minimization: ‖ A x − b ‖ 2 2 + ‖ Γ x ‖ 2 2 {\displaystyle \left\|A\mathbf {x} -\mathbf {b} \right\|_{2}^{2}+\left\|\Gamma \mathbf {x} \right\|_{2}^{2}} for some suitably chosen Tikhonov matrix Γ {\displaystyle \Gamma } . In many cases, this matrix

1404-526: A qualitatively new entity can be said to emerge—the general language of the working class... capitalism has the tendency of creating the general urban language of a given society. In 2010, there were 259.8 million speakers of Russian in the world: in Russia – 137.5 million, in the CIS and Baltic countries – 93.7 million, in Eastern Europe – 12.9 million, Western Europe – 7.3 million, Asia – 2.7 million, in

1512-467: A random variable distribution Tikhonov regularization , a method of regularization of ill-posed problems Tychonoff spaces , a completely regular topological spaces Tychonoff's theorem , a result on topological spaces Tychonoff separation axioms , in topology Other uses [ edit ] Tikhonov (rural locality) , a khutor in the Republic of Adygea, Russia Topics referred to by

1620-513: Is not a null matrix: x ∗ = x 0 + ( A T P A + Q ) − 1 ( A T P ( b − A x 0 ) ) . {\displaystyle \mathbf {x} ^{*}=\mathbf {x} _{0}+\left(A^{\mathsf {T}}PA+Q\right)^{-1}\left(A^{\mathsf {T}}P\left(\mathbf {b} -A\mathbf {x} _{0}\right)\right).} In some situations, one can avoid using

1728-471: Is ordinary least squares linear regression. However, if no x {\displaystyle \mathbf {x} } satisfies the equation or more than one x {\displaystyle \mathbf {x} } does—that is, the solution is not unique—the problem is said to be ill posed . In such cases, ordinary least squares estimation leads to an overdetermined , or more often an underdetermined system of equations. Most real-world phenomena have

1836-539: Is Belarusian, among ethnic Belarusians this share is 28.5%; the highest share of those who speak Belarusian at home is among ethnic Poles — 46.0%. In Estonia , Russian is spoken by 29.6% of the population, according to a 2011 estimate from the World Factbook, and is officially considered a foreign language. School education in the Russian language is a very contentious point in Estonian politics, and in 2022,

1944-481: Is a co-official language per article 5 of the Constitution of Kyrgyzstan . The 2009 census states that 482,200 people speak Russian as a native language, or 8.99% of the population. Additionally, 1,854,700 residents of Kyrgyzstan aged 15 and above fluently speak Russian as a second language, or 49.6% of the population in the age group. In Tajikistan , Russian is the language of inter-ethnic communication under

2052-401: Is a high degree of mutual intelligibility between Russian, Belarusian and Ukrainian , and a moderate degree of it in all modern Slavic languages, at least at the conversational level. Russian is written using a Cyrillic alphabet. The Russian alphabet consists of 33 letters. The following table gives their forms, along with IPA values for each letter's typical sound: Older letters of

2160-610: Is a post-posed definite article -to , -ta , -te similar to that existing in Bulgarian and Macedonian. In the Southern Russian dialects , instances of unstressed /e/ and /a/ following palatalized consonants and preceding a stressed syllable are not reduced to [ɪ] (as occurs in the Moscow dialect), being instead pronounced [a] in such positions (e.g. несл и is pronounced [nʲaˈslʲi] , not [nʲɪsˈlʲi] ) – this

2268-594: Is advantageous to the original Tikhonov regularization, since the Lavrentyev matrix A + Q {\displaystyle A+Q} can be better conditioned, i.e., have a smaller condition number , compared to the Tikhonov matrix A T A + Γ T Γ . {\displaystyle A^{\mathsf {T}}A+\Gamma ^{\mathsf {T}}\Gamma .} Typically discrete linear ill-conditioned problems result from discretization of integral equations , and one can formulate

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2376-488: Is being used less frequently by Russian-speaking typists in favor of the extension of Unicode character encoding , which fully incorporates the Russian alphabet. Free programs are available offering this Unicode extension, which allow users to type Russian characters, even on Western 'QWERTY' keyboards. The Russian language was first introduced to computing after the M-1 , and MESM models were produced in 1951. According to

2484-644: Is believed to be mostly continuous. This regularization improves the conditioning of the problem, thus enabling a direct numerical solution. An explicit solution, denoted by x ^ {\displaystyle {\hat {x}}} , is given by x ^ = ( A T A + Γ T Γ ) − 1 A T b . {\displaystyle {\hat {x}}=\left(A^{\mathsf {T}}A+\Gamma ^{\mathsf {T}}\Gamma \right)^{-1}A^{\mathsf {T}}\mathbf {b} .} The effect of regularization may be varied by

2592-624: Is called yakanye ( яканье ). Consonants include a fricative /ɣ/ , a semivowel /w⁓u̯/ and /x⁓xv⁓xw/ , whereas the Standard and Northern dialects have the consonants /ɡ/ , /v/ , and final /l/ and /f/ , respectively. The morphology features a palatalized final /tʲ/ in 3rd person forms of verbs (this is unpalatalized in the Standard and Northern dialects). During the Proto-Slavic (Common Slavic) times all Slavs spoke one mutually intelligible language or group of dialects. There

2700-410: Is chosen as a scalar multiple of the identity matrix ( Γ = α I {\displaystyle \Gamma =\alpha I} ), giving preference to solutions with smaller norms ; this is known as L 2 regularization . In other cases, high-pass operators (e.g., a difference operator or a weighted Fourier operator ) may be used to enforce smoothness if the underlying vector

2808-582: Is different from Wikidata All article disambiguation pages All disambiguation pages Russian language Russian is an East Slavic language belonging to the Balto-Slavic branch of the Indo-European language family . It is one of the four extant East Slavic languages, and is the native language of the Russians . It was the de facto and de jure official language of

2916-444: Is discussed below. Tikhonov regularization was invented independently in many different contexts. It became widely known through its application to integral equations in the works of Andrey Tikhonov and David L. Phillips. Some authors use the term Tikhonov–Phillips regularization . The finite-dimensional case was expounded by Arthur E. Hoerl , who took a statistical approach, and by Manus Foster, who interpreted this method as

3024-573: Is more spoken than English. Sizable Russian-speaking communities also exist in North America, especially in large urban centers of the US and Canada, such as New York City , Philadelphia , Boston , Los Angeles , Nashville , San Francisco , Seattle , Spokane , Toronto , Calgary , Baltimore , Miami , Portland , Chicago , Denver , and Cleveland . In a number of locations they issue their own newspapers, and live in ethnic enclaves (especially

3132-539: Is nothing but the Lagrange multiplier of the constraint. Typically, λ {\displaystyle \lambda } is chosen according to a heuristic criterion, so that the constraint will not be satisfied exactly. Specifically in the case of λ = 0 {\displaystyle \lambda =0} , in which the constraint is non-binding , the ridge estimator reduces to ordinary least squares . A more general approach to Tikhonov regularization

3240-564: Is odd") – чу́дно ( chúdno – "this is marvellous"), молоде́ц ( molodéts – "well done!") – мо́лодец ( mólodets – "fine young man"), узна́ю ( uznáyu – "I shall learn it") – узнаю́ ( uznayú – "I recognize it"), отреза́ть ( otrezát – "to be cutting") – отре́зать ( otrézat – "to have cut"); to indicate the proper pronunciation of uncommon words, especially personal and family names, like афе́ра ( aféra , "scandal, affair"), гу́ру ( gúru , "guru"), Гарси́я ( García ), Оле́ша ( Olésha ), Фе́рми ( Fermi ), and to show which

3348-592: Is possible to do so after the unregularised optimisation has taken place. E.g., if the above problem with Γ = 0 {\displaystyle \Gamma =0} yields the solution x ^ 0 {\displaystyle {\hat {x}}_{0}} , the solution in the presence of Γ ≠ 0 {\displaystyle \Gamma \neq 0} can be expressed as: x ^ = B x ^ 0 , {\displaystyle {\hat {x}}=B{\hat {x}}_{0},} with

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3456-402: Is recognized as a minority language under the Framework Convention for the Protection of National Minorities . Russian is the language of 9% of the population according to the World Factbook. Ethnologue cites Russian as the country's de facto working language. In China , Russian has no official status, but it is spoken by the small Russian communities in the northeastern Heilongjiang and

3564-569: Is sometimes considered to have played a significant role in the formation of modern Russian. Also, Russian has notable lexical similarities with Bulgarian due to a common Church Slavonic influence on both languages, but because of later interaction in the 19th and 20th centuries, Bulgarian grammar differs markedly from Russian. Over the course of centuries, the vocabulary and literary style of Russian have also been influenced by Western and Central European languages such as Greek, Latin , Polish , Dutch , German, French, Italian, and English, and to

3672-585: Is spoken by 14.2% of the population according to an undated estimate from the World Factbook. In 2005, Russian was the most widely taught foreign language in Mongolia, and was compulsory in Year 7 onward as a second foreign language in 2006. Around 1.5 million Israelis spoke Russian as of 2017. The Israeli press and websites regularly publish material in Russian and there are Russian newspapers, television stations, schools, and social media outlets based in

3780-432: Is the expected value of x {\displaystyle \mathbf {x} } , and Q {\displaystyle Q} is the inverse covariance matrix of x {\displaystyle \mathbf {x} } . The Tikhonov matrix is then given as a factorization of the matrix Q = Γ T Γ {\displaystyle Q=\Gamma ^{\mathsf {T}}\Gamma } (e.g.

3888-406: Is the regressand , X {\displaystyle \mathbf {X} } is the design matrix , I {\displaystyle \mathbf {I} } is the identity matrix , and the ridge parameter λ ≥ 0 {\displaystyle \lambda \geq 0} serves as the constant shifting the diagonals of the moment matrix. It can be shown that this estimator

3996-2042: Is the residual sum of squares , and τ {\displaystyle \tau } is the effective number of degrees of freedom . Using the previous SVD decomposition, we can simplify the above expression: RSS = ‖ y − ∑ i = 1 q ( u i ′ b ) u i ‖ 2 + ‖ ∑ i = 1 q α 2 σ i 2 + α 2 ( u i ′ b ) u i ‖ 2 , {\displaystyle \operatorname {RSS} =\left\|y-\sum _{i=1}^{q}(u_{i}'b)u_{i}\right\|^{2}+\left\|\sum _{i=1}^{q}{\frac {\alpha ^{2}}{\sigma _{i}^{2}+\alpha ^{2}}}(u_{i}'b)u_{i}\right\|^{2},} RSS = RSS 0 + ‖ ∑ i = 1 q α 2 σ i 2 + α 2 ( u i ′ b ) u i ‖ 2 , {\displaystyle \operatorname {RSS} =\operatorname {RSS} _{0}+\left\|\sum _{i=1}^{q}{\frac {\alpha ^{2}}{\sigma _{i}^{2}+\alpha ^{2}}}(u_{i}'b)u_{i}\right\|^{2},} and τ = m − ∑ i = 1 q σ i 2 σ i 2 + α 2 = m − q + ∑ i = 1 q α 2 σ i 2 + α 2 . {\displaystyle \tau =m-\sum _{i=1}^{q}{\frac {\sigma _{i}^{2}}{\sigma _{i}^{2}+\alpha ^{2}}}=m-q+\sum _{i=1}^{q}{\frac {\alpha ^{2}}{\sigma _{i}^{2}+\alpha ^{2}}}.} The probabilistic formulation of an inverse problem introduces (when all uncertainties are Gaussian)

4104-781: Is the solution to the least squares problem subject to the constraint β T β = c {\displaystyle \beta ^{\mathsf {T}}\beta =c} , which can be expressed as a Lagrangian: min β ( y − X β ) T ( y − X β ) + λ ( β T β − c ) {\displaystyle \min _{\beta }\,\left(\mathbf {y} -\mathbf {X} \beta \right)^{\mathsf {T}}\left(\mathbf {y} -\mathbf {X} \beta \right)+\lambda \left(\beta ^{\mathsf {T}}\beta -c\right)} which shows that λ {\displaystyle \lambda }

4212-518: Is the stressed word in a sentence, for example Ты́ съел печенье? ( Tý syel pechenye? – "Was it you who ate the cookie?") – Ты съе́л печенье? ( Ty syél pechenye? – "Did you eat the cookie?) – Ты съел пече́нье? ( Ty syel pechénye? "Was it the cookie you ate?"). Stress marks are mandatory in lexical dictionaries and books for children or Russian learners. The Russian syllable structure can be quite complex, with both initial and final consonant clusters of up to four consecutive sounds. Using

4320-508: Is then a self-adjoint bounded invertible operator. With Γ = α I {\displaystyle \Gamma =\alpha I} , this least-squares solution can be analyzed in a special way using the singular-value decomposition . Given the singular value decomposition A = U Σ V T {\displaystyle A=U\Sigma V^{\mathsf {T}}} with singular values σ i {\displaystyle \sigma _{i}} ,

4428-464: Is usually shown in writing not by a change of the consonant but rather by changing the following vowel. Another important aspect is the reduction of unstressed vowels . Stress , which is often unpredictable, is not normally indicated orthographically , though an optional acute accent may be used to mark stress – such as to distinguish between homographic words (e.g. замо́к [ zamók , 'lock'] and за́мок [ zámok , 'castle']), or to indicate

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4536-1202: Is usually unknown and often in practical problems is determined by an ad hoc method. A possible approach relies on the Bayesian interpretation described below. Other approaches include the discrepancy principle , cross-validation , L-curve method , restricted maximum likelihood and unbiased predictive risk estimator . Grace Wahba proved that the optimal parameter, in the sense of leave-one-out cross-validation minimizes G = RSS τ 2 = ‖ X β ^ − y ‖ 2 [ Tr ⁡ ( I − X ( X T X + α 2 I ) − 1 X T ) ] 2 , {\displaystyle G={\frac {\operatorname {RSS} }{\tau ^{2}}}={\frac {\left\|X{\hat {\beta }}-y\right\|^{2}}{\left[\operatorname {Tr} \left(I-X\left(X^{\mathsf {T}}X+\alpha ^{2}I\right)^{-1}X^{\mathsf {T}}\right)\right]^{2}}},} where RSS {\displaystyle \operatorname {RSS} }

4644-667: Is zero elsewhere. This demonstrates the effect of the Tikhonov parameter on the condition number of the regularized problem. For the generalized case, a similar representation can be derived using a generalized singular-value decomposition . Finally, it is related to the Wiener filter : x ^ = ∑ i = 1 q f i u i T b σ i v i , {\displaystyle {\hat {x}}=\sum _{i=1}^{q}f_{i}{\frac {u_{i}^{\mathsf {T}}b}{\sigma _{i}}}v_{i},} where

4752-470: The 2011 Lithuanian census , Russian was the native language for 7.2% of the population. In Moldova , Russian was considered to be the language of interethnic communication under a Soviet-era law. On 21 January 2021, the Constitutional Court of Moldova declared the law unconstitutional and deprived Russian of the status of the language of interethnic communication. 50% of the population

4860-1000: The Apollo–Soyuz mission, which first flew in 1975. In March 2013, Russian was found to be the second-most used language on websites after English. Russian was the language of 5.9% of all websites, slightly ahead of German and far behind English (54.7%). Russian was used not only on 89.8% of .ru sites, but also on 88.7% of sites with the former Soviet Union domain .su . Websites in former Soviet Union member states also used high levels of Russian: 79.0% in Ukraine, 86.9% in Belarus, 84.0% in Kazakhstan, 79.6% in Uzbekistan, 75.9% in Kyrgyzstan and 81.8% in Tajikistan. However, Russian

4968-701: The Cholesky factorization ) and is considered a whitening filter . This generalized problem has an optimal solution x ∗ {\displaystyle \mathbf {x} ^{*}} which can be written explicitly using the formula x ∗ = ( A T P A + Q ) − 1 ( A T P b + Q x 0 ) , {\displaystyle \mathbf {x} ^{*}=\left(A^{\mathsf {T}}PA+Q\right)^{-1}\left(A^{\mathsf {T}}P\mathbf {b} +Q\mathbf {x} _{0}\right),} or equivalently, when Q

5076-413: The Constitution of Tajikistan and is permitted in official documentation. 28% of the population was fluent in Russian in 2006, and 7% used it as the main language with family, friends or at work. The World Factbook notes that Russian is widely used in government and business. In Turkmenistan , Russian lost its status as the official lingua franca in 1996. Among 12% of the population who grew up in

5184-465: The Hermitian matrix A H {\displaystyle A^{\mathsf {H}}} . L 2 regularization is used in many contexts aside from linear regression, such as classification with logistic regression or support vector machines , and matrix factorization. Since Tikhonov Regularization simply adds a quadratic term to the objective function in optimization problems, it

5292-584: The Ukrainian language in more than 30 spheres of public life: in particular in public administration , media, education, science, culture, advertising, services . The law does not regulate private communication. A poll conducted in March 2022 by RATING in the territory controlled by Ukraine found that 83% of the respondents believe that Ukrainian should be the only state language of Ukraine. This opinion dominates in all macro-regions, age and language groups. On

5400-721: The United States Census , in 2007 Russian was the primary language spoken in the homes of over 850,000 individuals living in the United States. Russian is one of the official languages (or has similar status and interpretation must be provided into Russian) of the following: The Russian language is also one of two official languages aboard the International Space Station – NASA astronauts who serve alongside Russian cosmonauts usually take Russian language courses. This practice goes back to

5508-565: The fourth most widely used language on the Internet . Russian is written using the Russian alphabet of the Cyrillic script ; it distinguishes between consonant phonemes with palatal secondary articulation and those without—the so-called "soft" and "hard" sounds. Almost every consonant has a hard or soft counterpart, and the distinction is a prominent feature of the language, which

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5616-469: The "regularisation matrix" B = ( A T A + Γ T Γ ) − 1 A T A {\displaystyle B=\left(A^{\mathsf {T}}A+\Gamma ^{\mathsf {T}}\Gamma \right)^{-1}A^{\mathsf {T}}A} . If the parameter fit comes with a covariance matrix of the estimated parameter uncertainties V 0 {\displaystyle V_{0}} , then

5724-519: The 20th century, Russian was a mandatory language taught in the schools of the members of the old Warsaw Pact and in other countries that used to be satellites of the USSR. According to the Eurobarometer 2005 survey, fluency in Russian remains fairly high (20–40%) in some countries, in particular former Warsaw Pact countries. In Armenia , Russian has no official status, but it is recognized as

5832-471: The Belarusian society the Russian language prevails, so according to the 2019 census 6,718,557 people (71.4% of the total population) stated that they speak Russian at home, for ethnic Belarusians this share is 61.4%, for Russians — 97.2%, for Ukrainians — 89.0%, for Poles — 52.4%, and for Jews — 96.6%; 2,447,764 people (26.0% of the total population) stated that the language they usually speak at home

5940-532: The Great and developed from the Moscow ( Middle or Central Russian ) dialect substratum under the influence of some of the previous century's Russian chancery language. Prior to the Bolshevik Revolution , the spoken form of the Russian language was that of the nobility and the urban bourgeoisie. Russian peasants, the great majority of the population, continued to speak in their own dialects. However,

6048-590: The Institute of Russian Language of the Russian Academy of Sciences, an optional acute accent ( знак ударения ) may, and sometimes should, be used to mark stress . For example, it is used to distinguish between otherwise identical words, especially when context does not make it obvious: замо́к ( zamók – "lock") – за́мок ( zámok – "castle"), сто́ящий ( stóyashchy – "worthwhile") – стоя́щий ( stoyáshchy – "standing"), чудно́ ( chudnó – "this

6156-526: The Middle East and North Africa – 1.3 million, Sub-Saharan Africa – 0.1 million, Latin America – 0.2 million, U.S., Canada , Australia, and New Zealand – 4.1 million speakers. Therefore, the Russian language is the seventh-largest in the world by the number of speakers , after English, Mandarin, Hindi -Urdu, Spanish, French, Arabic, and Portuguese. Russian is one of the six official languages of

6264-807: The Russian alphabet include ⟨ ѣ ⟩ , which merged to ⟨ е ⟩ ( /je/ or /ʲe/ ); ⟨ і ⟩ and ⟨ ѵ ⟩ , which both merged to ⟨ и ⟩ ( /i/ ); ⟨ ѳ ⟩ , which merged to ⟨ ф ⟩ ( /f/ ); ⟨ ѫ ⟩ , which merged to ⟨ у ⟩ ( /u/ ); ⟨ ѭ ⟩ , which merged to ⟨ ю ⟩ ( /ju/ or /ʲu/ ); and ⟨ ѧ ⟩ and ⟨ ѩ ⟩ , which later were graphically reshaped into ⟨ я ⟩ and merged phonetically to /ja/ or /ʲa/ . While these older letters have been abandoned at one time or another, they may be used in this and related articles. The yers ⟨ ъ ⟩ and ⟨ ь ⟩ originally indicated

6372-458: The Russian principalities before and especially during Mongol rule. This strengthened dialectal differences, and for a while, prevented the emergence of a standardized national language. The formation of the unified and centralized Russian state in the 15th and 16th centuries, and the gradual re-emergence of a common political, economic, and cultural space created the need for a common standard language. The initial impulse for standardization came from

6480-990: The Soviet Union Mikhail Tikhonov , Soviet soldier and Hero of the Soviet Union Nikita Tikhonov, suspect in Stanislav Markelov murder case Nikolai Tikhonov , former Premier of the Soviet Union Nikolai Tikhonov (cosmonaut) , Russian cosmonaut Nikolai Tikhonov (writer) , Russian writer Vasily Tikhonov (pilot)  [ ru ] , Soviet pilot and Hero of the Soviet Union Vasily Tikhonov (rower) , Soviet rower Vasily Tikhonov (ice hockey) , Russian ice hockey coach Vasily Ivanovich Tikhonov  [ ru ] , Russian soldier and Hero of

6588-932: The Soviet Union Viktor Tikhonov (politician) , Ukrainian politician Viktor Pavlovich Tikhonov  [ ru ] , Soviet pilot and Hero of the Soviet Union Viktor Tikhonov (born 1930) , Russian ice hockey player and coach Viktor Tikhonov (born 1988) , Russian ice hockey player, Viktor Tikhonov's namesake and grandson Vladimir Tikhonov , Russian politician Vladimir Tikhonov (gymnast) , Soviet Olympic gymnast Vyacheslav Tikhonov (1928–2009), Soviet actor Anastasia Tikhonova , Russian tennis player Katerina Tikhonova , Russian scientist and manager Nina Tikhonova (1910–1995), Russian choreographic artist and dance instructor Sofia Tikhonova , Russian ski jumper Tamara Tikhonova , former Soviet Russian cross-country skier Mathematics [ edit ] Tikhonov distribution ,

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6696-458: The Soviet era can speak Russian, other generations of citizens that do not have any knowledge of Russian. Primary and secondary education by Russian is almost non-existent. In Uzbekistan , Russian is the language of inter-ethnic communication. It has some official roles, being permitted in official documentation and is the lingua franca of the country and the language of the elite. Russian

6804-503: The Tikhonov regularized solution can be expressed as x ^ = V D U T b , {\displaystyle {\hat {x}}=VDU^{\mathsf {T}}b,} where D {\displaystyle D} has diagonal values D i i = σ i σ i 2 + α 2 {\displaystyle D_{ii}={\frac {\sigma _{i}}{\sigma _{i}^{2}+\alpha ^{2}}}} and

6912-532: The Tikhonov-regularized solution is the most probable solution given the data and the a priori distribution of x {\displaystyle x} , according to Bayes' theorem . If the assumption of normality is replaced by assumptions of homoscedasticity and uncorrelatedness of errors , and if one still assumes zero mean, then the Gauss–Markov theorem entails that the solution

7020-467: The United Nations. Education in Russian is still a popular choice for both Russian as a second language (RSL) and native speakers in Russia, and in many former Soviet republics. Russian is still seen as an important language for children to learn in most of the former Soviet republics. In Belarus , Russian is a second state language alongside Belarusian per the Constitution of Belarus . 77% of

7128-516: The Wiener weights are f i = σ i 2 σ i 2 + α 2 {\displaystyle f_{i}={\frac {\sigma _{i}^{2}}{\sigma _{i}^{2}+\alpha ^{2}}}} and q {\displaystyle q} is the rank of A {\displaystyle A} . The optimal regularization parameter α {\displaystyle \alpha }

7236-403: The broader sense of expanding the use of Russian alongside or in favour of other languages. The current standard form of Russian is generally regarded as the modern Russian literary language ( современный русский литературный язык – "sovremenny russky literaturny yazyk"). It arose at the beginning of the 18th century with the modernization reforms of the Russian state under the rule of Peter

7344-501: The context of arbitrary likelihood fits, this is valid, as long as the quadratic approximation of the likelihood function is valid. This means that, as long as the perturbation from the unregularised result is small, one can regularise any result that is presented as a best fit point with a covariance matrix. No detailed knowledge of the underlying likelihood function is needed. For general multivariate normal distributions for x {\displaystyle \mathbf {x} } and

7452-572: The country. There is an Israeli TV channel mainly broadcasting in Russian with Israel Plus . See also Russian language in Israel . Russian is also spoken as a second language by a small number of people in Afghanistan . In Vietnam , Russian has been added in the elementary curriculum along with Chinese and Japanese and were named as "first foreign languages" for Vietnamese students to learn, on equal footing with English. The Russian language

7560-701: The data error, one can apply a transformation of the variables to reduce to the case above. Equivalently, one can seek an x {\displaystyle \mathbf {x} } to minimize ‖ A x − b ‖ P 2 + ‖ x − x 0 ‖ Q 2 , {\displaystyle \left\|A\mathbf {x} -\mathbf {b} \right\|_{P}^{2}+\left\|\mathbf {x} -\mathbf {x} _{0}\right\|_{Q}^{2},} where we have used ‖ x ‖ Q 2 {\displaystyle \left\|\mathbf {x} \right\|_{Q}^{2}} to stand for

7668-440: The effect of low-pass filters in the forward direction where A {\displaystyle A} maps x {\displaystyle \mathbf {x} } to b {\displaystyle \mathbf {b} } . Therefore, in solving the inverse-problem, the inverse mapping operates as a high-pass filter that has the undesirable tendency of amplifying noise ( eigenvalues / singular values are largest in

7776-435: The equations of inverse theory reduce to the equations above, with α = σ D / σ M {\displaystyle \alpha ={\sigma _{D}}/{\sigma _{M}}} . Although at first the choice of the solution to this regularized problem may look artificial, and indeed the matrix Γ {\displaystyle \Gamma } seems rather arbitrary,

7884-413: The factory and the industrial plant their local peasant dialects with their phonetics, grammar, and vocabulary, and the very process of recruiting workers from peasants and the mobility of the worker population generate another process: the liquidation of peasant inheritance by way of leveling the particulars of local dialects. On the ruins of peasant multilingual, in the context of developing heavy industry,

7992-456: The final reading amendments that state that all schools and kindergartens in the country are to transition to education in Latvian . From 2025, all children will be taught in Latvian only. On 28 September 2023, Latvian deputies approved The National Security Concept, according to which from 1 January 2026, all content created by Latvian public media (including LSM ) should be only in Latvian or

8100-717: The former Soviet Union . Russian has remained an official language of the Russian Federation , Belarus , Kazakhstan , Kyrgyzstan , and Tajikistan , and is still commonly used as a lingua franca in Ukraine , Moldova , the Caucasus , Central Asia , and to a lesser extent in the Baltic states and Israel . Russian has over 258 million total speakers worldwide. It is the most spoken native language in Europe ,

8208-552: The formula x ∗ = ( A + Q ) − 1 ( b + Q x 0 ) , {\displaystyle \mathbf {x} ^{*}=\left(A+Q\right)^{-1}\left(\mathbf {b} +Q\mathbf {x} _{0}\right),} which is nothing but the solution of the generalized Tikhonov problem where A = A T = P − 1 . {\displaystyle A=A^{\mathsf {T}}=P^{-1}.} The Lavrentyev regularization, if applicable,

8316-692: The generation of immigrants who started arriving in the early 1960s). Only about 25% of them are ethnic Russians, however. Before the dissolution of the Soviet Union , the overwhelming majority of Russophones in Brighton Beach, Brooklyn in New York City were Russian-speaking Jews. Afterward, the influx from the countries of the former Soviet Union changed the statistics somewhat, with ethnic Russians and Ukrainians immigrating along with some more Russian Jews and Central Asians. According to

8424-480: The government bureaucracy for the lack of a reliable tool of communication in administrative, legal, and judicial affairs became an obvious practical problem. The earliest attempts at standardizing Russian were made based on the so-called Moscow official or chancery language, during the 15th to 17th centuries. Since then, the trend of language policy in Russia has been standardization in both the restricted sense of reducing dialectical barriers between ethnic Russians, and

8532-459: The means are zero; their components are independent; the components have the same standard deviation σ x {\displaystyle \sigma _{x}} . The data are also subject to errors, and the errors in b {\displaystyle b} are also assumed to be independent with zero mean and standard deviation σ b {\displaystyle \sigma _{b}} . Under these assumptions

8640-414: The most spoken Slavic language , as well as the most geographically widespread language of Eurasia . It is the world's seventh-most spoken language by number of native speakers , and the world's ninth-most spoken language by total number of speakers . Russian is one of two official languages aboard the International Space Station , one of the six official languages of the United Nations , as well as

8748-524: The northwestern Xinjiang Uyghur Autonomous Region . Russian was also the main foreign language taught in school in China between 1949 and 1964. In Kazakhstan , Russian is not a state language, but according to article 7 of the Constitution of Kazakhstan its usage enjoys equal status to that of the Kazakh language in state and local administration. The 2009 census reported that 10,309,500 people, or 84.8% of

8856-515: The other hand, before the war, almost a quarter of Ukrainians were in favour of granting Russian the status of the state language, while after the beginning of Russia's invasion the support for the idea dropped to just 7%. In peacetime, the idea of raising the status of Russian was traditionally supported by residents of the south and east . But even in these regions, only a third of the respondents were in favour, and after Russia's full-scale invasion , their number dropped by almost half. According to

8964-461: The other three languages in the East Slavic branch. In many places in eastern and southern Ukraine and throughout Belarus, these languages are spoken interchangeably, and in certain areas traditional bilingualism resulted in language mixtures such as Surzhyk in eastern Ukraine and Trasianka in Belarus. An East Slavic Old Novgorod dialect , although it vanished during the 15th or 16th century,

9072-446: The parliament approved a bill to close up all Russian language schools and kindergartens by the school year. The transition to only Estonian language schools and kindergartens will start in the 2024-2025 school year. In Latvia , Russian is officially considered a foreign language. 55% of the population was fluent in Russian in 2006, and 26% used it as the main language with family, friends, or at work. On 18 February 2012, Latvia held

9180-453: The peasants' speech was never systematically studied, as it was generally regarded by philologists as simply a source of folklore and an object of curiosity. This was acknowledged by the noted Russian dialectologist Nikolai Karinsky , who toward the end of his life wrote: "Scholars of Russian dialects mostly studied phonetics and morphology. Some scholars and collectors compiled local dictionaries. We have almost no studies of lexical material or

9288-459: The population aged 15 and above, could read and write well in Russian, and understand the spoken language. In October 2023, Kazakhstan drafted a media law aimed at increasing the use of the Kazakh language over Russian, the law stipulates that the share of the state language on television and radio should increase from 50% to 70%, at a rate of 5% per year, starting in 2025. In Kyrgyzstan , Russian

9396-418: The population was fluent in Russian in 2006, and 67% used it as the main language with family, friends, or at work. According to the 2019 Belarusian census , out of 9,413,446 inhabitants of the country, 5,094,928 (54.1% of the total population) named Belarusian as their native language, with 61.2% of ethnic Belarusians and 54.5% of ethnic Poles declaring Belarusian as their native language. In everyday life in

9504-413: The process can be justified from a Bayesian point of view . Note that for an ill-posed problem one must necessarily introduce some additional assumptions in order to get a unique solution. Statistically, the prior probability distribution of x {\displaystyle x} is sometimes taken to be a multivariate normal distribution . For simplicity here, the following assumptions are made:

9612-479: The pronunciation of ultra-short or reduced /ŭ/ , /ĭ/ . Because of many technical restrictions in computing and also because of the unavailability of Cyrillic keyboards abroad, Russian is often transliterated using the Latin alphabet. For example, мороз ('frost') is transliterated moroz , and мышь ('mouse'), mysh or myš' . Once commonly used by the majority of those living outside Russia, transliteration

9720-472: The proper pronunciation of uncommon words or names. Russian is an East Slavic language of the wider Indo-European family . It is a descendant of Old East Slavic , a language used in Kievan Rus' , which was a loose conglomerate of East Slavic tribes from the late 9th to the mid-13th centuries. From the point of view of spoken language , its closest relatives are Ukrainian , Belarusian , and Rusyn ,

9828-492: The regularisation matrix will be B = ( V 0 − 1 + Γ T Γ ) − 1 V 0 − 1 , {\displaystyle B=(V_{0}^{-1}+\Gamma ^{\mathsf {T}}\Gamma )^{-1}V_{0}^{-1},} and the regularised result will have a new covariance V = B V 0 B T . {\displaystyle V=BV_{0}B^{\mathsf {T}}.} In

9936-491: The respondents), while according to the 2002 census – 142.6 million people (99.2% of the respondents). In Ukraine , Russian is a significant minority language. According to estimates from Demoskop Weekly, in 2004 there were 14,400,000 native speakers of Russian in the country, and 29 million active speakers. 65% of the population was fluent in Russian in 2006, and 38% used it as the main language with family, friends, or at work. On 5 September 2017, Ukraine's Parliament passed

10044-472: The reverse mapping where they were smallest in the forward mapping). In addition, ordinary least squares implicitly nullifies every element of the reconstructed version of x {\displaystyle \mathbf {x} } that is in the null-space of A {\displaystyle A} , rather than allowing for a model to be used as a prior for x {\displaystyle \mathbf {x} } . Ordinary least squares seeks to minimize

10152-545: The same term [REDACTED] This disambiguation page lists articles associated with the title Tikhonov . If an internal link led you here, you may wish to change the link to point directly to the intended article. Retrieved from " https://en.wikipedia.org/w/index.php?title=Tikhonov&oldid=1258255448 " Categories : Disambiguation pages Disambiguation pages with surname-holder lists Russian-language surnames Hidden categories: Articles containing Russian-language text Short description

10260-456: The scale of matrix Γ {\displaystyle \Gamma } . For Γ = 0 {\displaystyle \Gamma =0} this reduces to the unregularized least-squares solution, provided that ( A A ) exists. Note that in case of a complex matrix A {\displaystyle A} , as usual the transpose A T {\displaystyle A^{\mathsf {T}}} has to be replaced by

10368-813: The simplest case, the problem of a near-singular moment matrix X T X {\displaystyle \mathbf {X} ^{\mathsf {T}}\mathbf {X} } is alleviated by adding positive elements to the diagonals , thereby decreasing its condition number . Analogous to the ordinary least squares estimator, the simple ridge estimator is then given by β ^ R = ( X T X + λ I ) − 1 X T y {\displaystyle {\hat {\beta }}_{R}=\left(\mathbf {X} ^{\mathsf {T}}\mathbf {X} +\lambda \mathbf {I} \right)^{-1}\mathbf {X} ^{\mathsf {T}}\mathbf {y} } where y {\displaystyle \mathbf {y} }

10476-475: The sum of squared residuals , which can be compactly written as ‖ A x − b ‖ 2 2 , {\displaystyle \left\|A\mathbf {x} -\mathbf {b} \right\|_{2}^{2},} where ‖ ⋅ ‖ 2 {\displaystyle \|\cdot \|_{2}} is the Euclidean norm . In order to give preference to

10584-679: The survey carried out by RATING in August 2023 in the territory controlled by Ukraine and among the refugees, almost 60% of the polled usually speak Ukrainian at home, about 30% – Ukrainian and Russian, only 9% – Russian. Since March 2022, the use of Russian in everyday life has been noticeably decreasing. For 82% of respondents, Ukrainian is their mother tongue, and for 16%, Russian is their mother tongue. IDPs and refugees living abroad are more likely to use both languages for communication or speak Russian. Nevertheless, more than 70% of IDPs and refugees consider Ukrainian to be their native language. In

10692-459: The syntax of Russian dialects." After 1917, Marxist linguists had no interest in the multiplicity of peasant dialects and regarded their language as a relic of the rapidly disappearing past that was not worthy of scholarly attention. Nakhimovsky quotes the Soviet academicians A.M Ivanov and L.P Yakubinsky, writing in 1930: The language of peasants has a motley diversity inherited from feudalism. On its way to becoming proletariat peasantry brings to

10800-465: The transpose A T {\displaystyle A^{\mathsf {T}}} , as proposed by Mikhail Lavrentyev . For example, if A {\displaystyle A} is symmetric positive definite, i.e. A = A T > 0 {\displaystyle A=A^{\mathsf {T}}>0} , so is its inverse A − 1 {\displaystyle A^{-1}} , which can thus be used to set up

10908-786: The two. Others divide the language into three groupings, Northern , Central (or Middle), and Southern , with Moscow lying in the Central region. The Northern Russian dialects and those spoken along the Volga River typically pronounce unstressed /o/ clearly, a phenomenon called okanye ( оканье ). Besides the absence of vowel reduction, some dialects have high or diphthongal /e⁓i̯ɛ/ in place of Proto-Slavic  * ě and /o⁓u̯ɔ/ in stressed closed syllables (as in Ukrainian) instead of Standard Russian /e/ and /o/ , respectively. Another Northern dialectal morphological feature

11016-511: The use of the language has some presence in certain areas. A large part of the population, especially the older generations, can speak Russian as a foreign language. However, English has replaced Russian as lingua franca in Lithuania and around 80% of young people speak English as their first foreign language. In contrast to the other two Baltic states, Lithuania has a relatively small Russian-speaking minority (5.0% as of 2008). According to

11124-731: The weighted norm squared ‖ x ‖ P 2 = x T A − 1 x {\displaystyle \left\|\mathbf {x} \right\|_{P}^{2}=\mathbf {x} ^{\mathsf {T}}A^{-1}\mathbf {x} } in the generalized Tikhonov regularization, leading to minimizing ‖ A x − b ‖ A − 1 2 + ‖ x − x 0 ‖ Q 2 {\displaystyle \left\|A\mathbf {x} -\mathbf {b} \right\|_{A^{-1}}^{2}+\left\|\mathbf {x} -\mathbf {x} _{0}\right\|_{Q}^{2}} or, equivalently up to

11232-493: The weighted norm squared x T Q x {\displaystyle \mathbf {x} ^{\mathsf {T}}Q\mathbf {x} } (compare with the Mahalanobis distance ). In the Bayesian interpretation P {\displaystyle P} is the inverse covariance matrix of b {\displaystyle \mathbf {b} } , x 0 {\displaystyle \mathbf {x} _{0}}

11340-402: Was developed as a possible solution to the imprecision of least square estimators when linear regression models have some multicollinear (highly correlated) independent variables—by creating a ridge regression estimator (RR). This provides a more precise ridge parameters estimate, as its variance and mean square estimator are often smaller than the least square estimators previously derived. In

11448-405: Was first introduced in North America when Russian explorers voyaged into Alaska and claimed it for Russia during the 18th century. Although most Russian colonists left after the United States bought the land in 1867, a handful stayed and preserved the Russian language in this region to this day, although only a few elderly speakers of this unique dialect are left. In Nikolaevsk, Alaska , Russian

11556-421: Was fluent in Russian in 2006, and 19% used it as the main language with family, friends, or at work. According to the 2014 Moldovan census , Russians accounted for 4.1% of Moldova's population, 9.4% of the population declared Russian as their native language, and 14.5% said they usually spoke Russian. According to the 2010 census in Russia , Russian language skills were indicated by 138 million people (99.4% of

11664-402: Was the sixth-most used language on the top 1,000 sites, behind English, Chinese, French, German, and Japanese. Despite leveling after 1900, especially in matters of vocabulary and phonetics, a number of dialects still exist in Russia. Some linguists divide the dialects of Russian into two primary regional groupings, "Northern" and "Southern", with Moscow lying on the zone of transition between

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