An introduction to numerical analysis / Kendall E. Atkinson.
Editor: New York : Wiley, c1978Descripción: xiii, 587 p. : il. ; 24 cmISBN: 0471029859Tema(s): Numerical analysisOtra clasificación: 65-01ONE THE SOURCES AND PROPAGATION OF ERRORS [3] 1.1 Mathematical Preliminaries [3] 1.2 Computer Representation of Numbers [12] 1.3 Sources of Error [14] 1.4 Propagation of Errors [19] 1.5 Stability in Numerical Analysis [26] Discussion of the Literature [32] Problems [34] TWO ROOTFINDING FOR NONLINEAR EQUATIONS [39] 2.1 Simple Enclosure Methods [42] 2.2 The Secant Method [48] 2.3 Newton’s Method [52] 2.4 A General Theory for One-Point Iteration Methods [58] 2.5 Aitken Extrapolation for Linearly Convergent Sequences [65] 2.6 Error Tests [68] 2.7 The Numerical Evaluation of Multiple Roots [71] 8.8 Brent’s Rootfinding Algorithm [75] 2.9 Roots of Polynomials [78] 2.10 Muller’s Method [85] 2.11 Nonlinear Systems of Equations [88] 2.12 Newton’s Method for Nonlinear Systems [92] Discussion of the Literature [95] Problems [97] THREE INTERPOLATION THEORY 107 [107] 3.1 Polynomial Interpolation Theory 3.2 Newton Divided Differences [114] 3.3 Finite Differences and Table-Oriented Interpolation Formulas [123] 3.4 Errors in Data and Forward Differences [129] 3.5 Further Results on Interpolation Error [132] 3.6 Hermite Interpolation [137] 3.7 Piecewise Polynomial Interpolation [141] Discussion of the Literature [150] Problems [153] FOUR APPROXIMATION OF FUNCTIONS [161] 4.1 The Weierstrass Theorem and Taylor’s Theorem [162] 4.2 The Minimax Approximation Problem [165] 4.3 The Least Squares Approximation Problem [168] 4.4 Orthogonal Polynomials [171] 4.5 The Least Squares Approximation Problem (continued) [180] 4.6 Economization of Taylor Series [186] 4.7 Minimax Approximations [190] 4.8 Near-Minimax Approximations [194] 4.9 The Remes Algorithm [201] Discussion of the Literature [203] Problems [205] FIVE NUMERICAL INTEGRATION [213] 5.1 The Trapezoidal Rule and Simpson’s Rule [215] 5.2 Newton-Cotes Integration Formulas [225] 5.3 Gaussian Quadrature [231] 5.4 Patterson’s Method [243] 5.5 Asymptotic Error Formulas and Their Application [248] 5.6 Adaptive Numerical Integration [263] 5.7 Singular Integrals [268] Discussion of the Literature [277] Problems [279] SIX NUMERICAL METHODS FOR DIFFERENTIAL EQUATIONS [289] 6.1 Existence, Uniqueness, and Stability Theory [292] 6.2 Euler’s Method [300] 6.3 Multistep Methods [314] 6.4 The Midpoint Method [320] 6.5 The Trapezoidal Method [325] 6.6 A Low-Order Predictor-Corrector Algorithm [330] 6.7 Derivation of Higher-Order Multistep Methods [338] 6.8 Convergence and Stability Theory for Multistep Methods [350] 6.9 Single-Step and Runge-Kutta Methods [366] Discussion of Literature [380] Problems [384] SEVEN LINEAR ALGEBRA [393] 7.1 Vector Spaces, Matrices, and Linear Systems [393] 7.2 Eigenvalues and Canonical Forms for Matrices [401] 7.3 Vector and Matrix Norms [412] 7.4 Convergence and Perturbation Theorems [421] Discussion of Literature [427] Problems [428] EIGHT NUMERICAL SOLUTION OF SYSTEMS OF LINEAR EQUATIONS [435] 8.1 Gaussian Elimination [436] 8.2 Pivoting and Scaling in Gaussian Elimination [444] 8.3 Variants of Gaussian Elimination [450] 8.4 Error Analysis [457] 8.5 The Residual Correction Method [467] 8.6 Iteration Methods [471] 8.7 Error Prediction and Acceleration [478] 8.8 The Numerical Solution of Poisson’s Equation [482] Discussion of Literature [487] Problems [490] NINE THE MATRIX EIGENVALUE PROBLEM [499] 9.1 Eigenvalue Location, Error, and Stability Results [500] 9.2 The Power Method [514] 9.3 Orthogonal Transformations Using Householder Matrices [521] 9.4 The Eigenvalues of a Symmetric Tridiagonal Matrix [532] 9.5 The QR Method [539] 9.6 The Calculation of Eigenvectors and Inverse Iteration [548] Discussion of Literature [553] Problems [551] ANSWERS TO SELECTED EXERCISES [561]
| Item type | Home library | Shelving location | Call number | Materials specified | Status | Date due | Barcode | Course reserves |
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Instituto de Matemática, CONICET-UNS | Libros ordenados por tema | 65 At875 (Browse shelf) | Available | A-5157 |
Incluye referencias bibliográficas e índice.
ONE --
THE SOURCES AND PROPAGATION OF ERRORS [3] --
1.1 Mathematical Preliminaries [3] --
1.2 Computer Representation of Numbers [12] --
1.3 Sources of Error [14] --
1.4 Propagation of Errors [19] --
1.5 Stability in Numerical Analysis [26] --
Discussion of the Literature [32] --
Problems [34] --
TWO --
ROOTFINDING FOR NONLINEAR EQUATIONS [39] --
2.1 Simple Enclosure Methods [42] --
2.2 The Secant Method [48] --
2.3 Newton’s Method [52] --
2.4 A General Theory for One-Point Iteration Methods [58] --
2.5 Aitken Extrapolation for Linearly Convergent Sequences [65] --
2.6 Error Tests [68] --
2.7 The Numerical Evaluation of Multiple Roots [71] --
8.8 Brent’s Rootfinding Algorithm [75] --
2.9 Roots of Polynomials [78] --
2.10 Muller’s Method [85] --
2.11 Nonlinear Systems of Equations [88] --
2.12 Newton’s Method for Nonlinear Systems [92] --
Discussion of the Literature [95] --
Problems [97] --
--
THREE --
INTERPOLATION THEORY 107 [107] --
3.1 Polynomial Interpolation Theory --
3.2 Newton Divided Differences [114] --
3.3 Finite Differences and Table-Oriented Interpolation Formulas [123] --
3.4 Errors in Data and Forward Differences [129] --
3.5 Further Results on Interpolation Error [132] --
3.6 Hermite Interpolation [137] --
3.7 Piecewise Polynomial Interpolation [141] --
Discussion of the Literature [150] --
Problems [153] --
FOUR --
APPROXIMATION OF FUNCTIONS [161] --
4.1 The Weierstrass Theorem and Taylor’s Theorem [162] --
4.2 The Minimax Approximation Problem [165] --
4.3 The Least Squares Approximation Problem [168] --
4.4 Orthogonal Polynomials [171] --
4.5 The Least Squares Approximation Problem (continued) [180] --
4.6 Economization of Taylor Series [186] --
4.7 Minimax Approximations [190] --
4.8 Near-Minimax Approximations [194] --
4.9 The Remes Algorithm [201] --
Discussion of the Literature [203] --
Problems [205] --
FIVE --
NUMERICAL INTEGRATION [213] --
5.1 The Trapezoidal Rule and Simpson’s Rule [215] --
5.2 Newton-Cotes Integration Formulas [225] --
5.3 Gaussian Quadrature [231] --
5.4 Patterson’s Method [243] --
5.5 Asymptotic Error Formulas and Their Application [248] --
5.6 Adaptive Numerical Integration [263] --
5.7 Singular Integrals [268] --
Discussion of the Literature [277] --
Problems [279] --
SIX --
NUMERICAL METHODS FOR DIFFERENTIAL EQUATIONS [289] --
6.1 Existence, Uniqueness, and Stability Theory [292] --
6.2 Euler’s Method [300] --
6.3 Multistep Methods [314] --
6.4 The Midpoint Method [320] --
6.5 The Trapezoidal Method [325] --
6.6 A Low-Order Predictor-Corrector Algorithm [330] --
6.7 Derivation of Higher-Order Multistep Methods [338] --
6.8 Convergence and Stability Theory for Multistep Methods [350] --
6.9 Single-Step and Runge-Kutta Methods [366] --
Discussion of Literature [380] --
Problems [384] --
SEVEN --
LINEAR ALGEBRA [393] --
7.1 Vector Spaces, Matrices, and Linear Systems [393] --
7.2 Eigenvalues and Canonical Forms for Matrices [401] --
7.3 Vector and Matrix Norms [412] --
7.4 Convergence and Perturbation Theorems [421] --
Discussion of Literature [427] --
Problems [428] --
EIGHT --
NUMERICAL SOLUTION OF SYSTEMS OF LINEAR EQUATIONS [435] --
8.1 Gaussian Elimination [436] --
8.2 Pivoting and Scaling in Gaussian Elimination [444] --
8.3 Variants of Gaussian Elimination [450] --
8.4 Error Analysis [457] --
8.5 The Residual Correction Method [467] --
8.6 Iteration Methods [471] --
8.7 Error Prediction and Acceleration [478] --
8.8 The Numerical Solution of Poisson’s Equation [482] --
Discussion of Literature [487] --
Problems [490] --
NINE --
THE MATRIX EIGENVALUE PROBLEM [499] --
9.1 Eigenvalue Location, Error, and Stability Results [500] --
9.2 The Power Method [514] --
9.3 Orthogonal Transformations Using Householder Matrices [521] --
9.4 The Eigenvalues of a Symmetric Tridiagonal Matrix [532] --
9.5 The QR Method [539] --
9.6 The Calculation of Eigenvectors and Inverse Iteration [548] --
Discussion of Literature [553] --
Problems [551] --
ANSWERS TO SELECTED EXERCISES [561] --
MR, 80a:65001
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