The Application of Continued Fractions And Their Generalizations To Problems In Approximation Theory
| Автор(ы): | Khovanskii A. N.
06.10.2007
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| 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. |
| Оглавление: |
Обложка книги.
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] |
| Формат: | djvu |
| Размер: | 1289658 байт |
| Язык: | ENG |
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