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Snyder M.A. — Chebyshev methods in numerical approximation
Snyder M.A. — Chebyshev methods in numerical approximation

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Название: Chebyshev methods in numerical approximation

Автор: Snyder M.A.

Язык: en

Рубрика: Математика/

Статус предметного указателя: Готов указатель с номерами страниц

ed2k: ed2k stats

Год издания: 1966

Количество страниц: 125

Добавлена в каталог: 25.11.2012

Операции: Положить на полку | Скопировать ссылку для форума | Скопировать ID
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Предметный указатель
Addition formula      26 98
Approximation, reasons for      1 2
Arctangent, Chebyshev series for      35 51 52
Bessel functions      45 46 47 56 93—96
Bessel functions, Chebyshev expansions of      49
Bessel functions, differential recurrence relation      20
Bessel functions, Fourier transform of      25
Bessel functions, relation to Chebyshev polynomials      19 20 35 47—49 101
Chebyshev differential equation      12 13 23 98
Chebyshev expansions of absolute value function      56
Chebyshev expansions of algebraic powers      45
Chebyshev expansions of arctangent      35 51 52
Chebyshev expansions of Bessel functions      47—49
Chebyshev expansions of cosine      47
Chebyshev expansions of delta distribution      56
Chebyshev expansions of exponential      45 49
Chebyshev expansions of hyperbolic cosine      47
Chebyshev expansions of hyperbolic sine      46
Chebyshev expansions of inverse monomials      49 50
Chebyshev expansions of logarithm      50 52
Chebyshev expansions of sign function      56
Chebyshev expansions of sine      46
Chebyshev expansions, coefficients of      29 100 102
Chebyshev functions      13
Chebyshev polynomials and analytic functions      30 101
Chebyshev polynomials and Bessel functions      19 20 47— 49 101
Chebyshev polynomials and continued fractions      78 80 81 82
Chebyshev polynomials and difference equations      57
Chebyshev polynomials and economization of continued fractions      82—86
Chebyshev polynomials and economization of power series      36—39
Chebyshev polynomials and hypergeometric functions      25 98
Chebyshev polynomials and matrices      26
Chebyshev polynomials and optimal approximation      55
Chebyshev polynomials and powers      36 39 40 45 100 102 104 105
Chebyshev polynomials and trigonometric functions      9 13 45—47 97
Chebyshev polynomials and ultraspherical polynomials      8 32 33
Chebyshev polynomials of the first kind      8 9 11 19 39 102
Chebyshev polynomials of the second kind      21 22 23 102 103
Chebyshev polynomials, addition formula      26 98
Chebyshev polynomials, and hyperbolic functions      46 47 111
Chebyshev polynomials, behavior near      1 18
Chebyshev polynomials, completeness      27—28
Chebyshev polynomials, derivatives of      22 23 101
Chebyshev polynomials, expansions in      29 30 32 33 44—56 100 102
Chebyshev polynomials, explicit representations      9 14 18 21 23 24 25 99 102 103 104
Chebyshev polynomials, functional equations      15 26 98
Chebyshev polynomials, generating functions      15—16 23 26 44 99
Chebyshev polynomials, integrals of      15 20 23 63 100 102
Chebyshev polynomials, multiplication formulas      15 99
Chebyshev polynomials, orthogonality of      16 20 29 98 101
Chebyshev polynomials, partial fraction decomposition      25 101
Chebyshev polynomials, products of powers with      15 21 40 102
Chebyshev polynomials, rational expressions in      10 80 81
Chebyshev polynomials, recurrence relations      9 15 22 25 97 98
Chebyshev polynomials, Rodrigue’s formula      16 47 101
Chebyshev polynomials, shifted, of the first kind      20 21 40 62 63 101 103
Chebyshev polynomials, shifted, of the second kind      22 24 101 104
Chebyshev polynomials, summation of series in      34 35 100 101 102
Chebyshev polynomials, summation orthogonality      30
Chebyshev polynomials, zeros of      14 25 101
Chebyshev’s theorem      31 32
Completeness      27—28
Continued fractions      9 10 78
Continued fractions and differential equations      76—78
Continued fractions, accelerated convergence of      72 73
Continued fractions, classic expansions      69—72
Continued fractions, convergence of      68 69
Continued fractions, conversion to      66 81
Continued fractions, evaluation on computer      10
Continued fractions, Thiele expansions      73—76
Contour integrals      12 48 93 94
Convergence of continued fractions      68 69
Delta distribution      56 57
Delta, Kronecker      6 16
Derivative of Chebyshev polynomials      22 23 101
Derivative, inverse      73
Derivative, reciprocal      73
Difference equations      41 50 57 91 92
Difference, reciprocal      73
Difference, symmetric      73
Differential equations and continued fractions      76—78
Differential equations and tau method      42—43
Differential equations, Chebyshev      12—13 14 23 98
Dirac delta function      56 57
Economization of continued fractions      82—86
Economization of power series      36—39
Error curve, standard form      87
Expansions      (see Chebyshev expansions)
Exponential function      1 45
Exponential function, Chebyshev series for      45 49
Exponential function, economized series for      4 37 38 39
Exponential integral function      42—44
Functional equations      15 26 98
Gauss duplication formula      48
Generating functions      15—16 23 26 44 99
Hyperbolic functions      46 47
Hypergeometric function      25 98
Integrals of Chebyshev polynomials      15 20 23 63 100 102
Inverse tangent      (see Arctangent)
Kopal’s method      61—63
Kronecker delta      6 16
Lanczos      (see Tau method)
Least squares norm      3 6
Least squares norm of Legendre polynomials      7
Legendre polynomials      6 7
Legendre polynomials, expansions in      7 34
Logarithm, Chebyshev series for      50 52
Logarithm, rational approximations to      60 62 63 65 66
Maehly’s method      80—82
Matrix and Chebyshev polynomials      26
Maximum norm      3 4
minimax      (see Optimal approximations)
Multiplication formulas      15 99
Norms      3
ObreschkofFs formula      63—66
ObreschkofFs formula, optimal      86
Optimal approximations, form of error      4
Optimal approximations, polynomials      53—55
Optimal approximations, rational      86—89
Orthogonal polynomials      5 6 7 34
Orthogonality of Chebyshev polynomials      16 20 29 98 101
Orthogonality of Legendre polynomials      6
Orthogonality of ultraspherical polynomials      8 32
Orthogonality, under summation      30
pade      58—60
Pade approximation      58—60
Pade of power function      65
Pade of square root function      61
Pade table      59
Partial fractions      25 101
Polynomials, Chebyshev      (see Chebyshev polynomials)
Polynomials, evaluation of      2
Polynomials, Legendre      6 7 34
Polynomials, minimax      53
Polynomials, optimal      53
Polynomials, orthogonal      5 6 7 34
Polynomials, ultraspherical      8 32 33
Polynomials, zeros of      7 14 25 101
Powers, as combinations of Chebyshev polynomials      36 39 40 45 100 104 105
Products of powers and Chebyshev polynomials      15 21 40 102
Rational approximation by iteration      60 61
Rational approximation of exponential function      65
Rational approximation of logarithm function      60 62 63 65 66
Rational approximation with Chebyshev polynomials      10 80 81
Rational approximation, advantages of      9
Rational approximation, conversion to continued fractions      66—68
Rational approximation, Kopal’s method      61—63
Rational approximation, minimax      86
Recurrence relations for Chebyshev polynomials      9 15 22 25 97 98
Recurrence relations for Legendre polynomials      6
Recurrence relations for modified Bessel functions      20
Ricatti equation      76
Rodigue’s formula for Chebyshev polynomials      16 47 101
Rodigue’s formula for Legendre polynomials      6
Rodigue’s formula for ultraspherical polynomials      8 32
Shifted polynomials      (see Chebyshev polynomials)
Sign function      56
Summation of series      34 100 101 102
Summation orthogonality      30
Tau method      40—44 49 61
Taylor’s series      1 5 64
Taylor’s series, inadequacy of      4 5 34 54
Taylor’s series, relation to ultraspherical polynomials      8 34
Thiele expansions      73—76
Trigonometric functions      9 13 46 47 97
Ultraspherical polynomials      8 32 33
Zeros of Chebyshev polynomials      14 25 101
Zeros of orthogonal polynomials      7
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