The Application of Continued Fractions And Their Generalizations To Problems In Approximation Theory (Khovanskii A. N.)

The Application of Continued Fractions And Their Generalizations To Problems In Approximation Theory

Автор(ы):Khovanskii A. N.
06.10.2007
Описание: Стоят у таверны трое варваров, разговаривают: Крэг Хэк (шепотом): Уважаемый коллега, несмотря на то, что обе приведенные тобой в модели включает в себя лагированные значения переменных, следует заметить, что они существенно отличаются с точки зрения статистического оценивания параметров! В первом уравнении регрессоры некоррелированы с ошибками, поэтому эту модель можно оценивать с помощью метода наименьших квадратов. Во второй же модели yt-1 включает в себя ошибку ut-1, следовательно, вектор ошибок u и матрица регрессоров X коррелированны. В этом случае МНК-оценка будет смещенной и несостоятельной! Килдор (шепотом): Вот именно, коллега! Первая модель – пример модели распределенных лагов. Вторая же модель – пример авторегрессионной модели распределенных лагов. Взяв эти модели я… Йог (шепотом): Коллеги, внимание - к нам приближаются маги! Килдор (в полный голос): …ну дык вот я ж и грю, шо узяв я адну фотамадель за сиськи, а другую за *опу… Вот приблизительно об этом и эта книга.
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The Application of Continued Fractions And Their Generalizations To Problems In Approximation Theory — обложка книги. Обложка книги.
CHAPTER I
Certain Problems in the Theory of Continued Fractions
§ 1. Convergents [1]
§ 2. Transformations of Continued Fractions [9]
§ 3. The Transformation of Series into Continued Fractions [23]
§ 4. General Considerations in the Convergence Theory of Continued Fractions [31]
§ 5. Convergence Tests for Continued Fractions with Positive Coefficients [42]
§ 6. Convergence Tests for Continued Fractions with Arbitrary Coefficients [46]
§ 7. Convergence Tests for Continued Fractions which are Periodic in the Limit [58]
CHAPTER II
Continued Fraction Expansions of Certain Functions
§ 1. A Solution of a Certain Riccati Equation with the help of Continued Fractions [76]
§ 2. Continued Fraction Expansions of Binomial Functions [100]
§ 3. The Continued Fraction Expansion of fyx [109]
§ 4. Continued Fraction Expansions of the Natural Logarithm [110]
§ 5. Continued Fraction Expansions of ez [112]
§ 6. Continued Fraction Expansions of the Inverse Trigonometric and Hyperbolic Functions [114]
§ 7. Continued Fraction Expansions for tan x and tanh x . [122]
§ 8. The Continued Fraction Expansion of the Integral (формула) [125]
§ 9. The Solution of the Equations of Boole and Riccati with the help of Continued Fractions [130]
§ 10. Continued Fractions and the Hypergeometric Series [133]
§ 11. Continued Fraction Expansions of Prym's Function [142]
§ 12. The Continued Fraction Expansion of the Incomplete Gamma-Function [148]
CHAPTER III
Further Methods for Obtaining Rational Function Approximations
§ 1. Obreschkoff's Formula [151]
§ 2. The Derivation of Rational Function Approximations to Certain Functions with the Help of Obreschkoff's Formula [155]
§ 3. The Solution of Certain Difference Equations with the Help of Continued Fractions [159]
§ 4. The Derivation of Rational Function Approximations by means of Iteration [163]
§ 5. Table of Approximate Values of (?) [165]
§ 6. Table of Approximate Values of In x; [166]
§ 7. Table of Approximate Values of tan x and tanh x [167]
§ 8. Rational Function Approximations for sinh x and sin x [167]
§ 9. Rational Function Approximations for cosh A: and cos A: [171]
§ 10. Rational Function Approximations to the Error Function [174]
§ 11. The Continued Fraction Expansion of Stirling's Series [175]
§ 12. Rational Function Approximations for Г( 1 + x) [177]
CHAPTER IV
Generalized Continued Fractions
§ 1. The Computation of Square Roots with the Help of Matrices of the Second Order [182]
§ 2. The Solution of Quadratic Equations with the Help of Matrices of the Second Order [188]
§ 3. The Calculation of Cube Roots with the Help of Matrices [194]
§ 4. The Calculation of Fourth Roots with the Help otMatrices [196]
§ 5. The Calculation of Roots of Arbitrary Rational Orderwith the Help of a Matrix [198]
§ 6. The Solution of Cubic Equations with the Help of Matrices [199]
§ 7. The Solution of Equations of Higher Order with the Help of Matrices [201]
LITERATURE IN THE RUSSIAN LANGUAGE ON THE GENERAL
THEORY OF CONTINUED FRACTIONS [203]
REFERENCES [204]
SUPPLEMENTARY REFERENCES [210]
INDEX [211]
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