Numerical analysis / Richard L. Burden, J. Douglas Faires.
Series The Prindle, Weber & Schmidt series in mathematicsEditor: Boston : PWS-Kent Pub. Co., c1993Edición: 5th edDescripción: xiv, 768 p. : il. (algunas col.) ; 24 cmISBN: 0534932193Tema(s): Numerical analysisOtra clasificación: 65-011 Mathematical Preliminaries [1] 1.1 Review of Calculus [2] 1.2 Round-Off Errors and Computer Arithmetic [12] 1.3 Algorithms and Convergence [24] 1.4 Numerical Software [32] 2 Solutions of Equations in One Variable [39] 2.1 The Bisection Method [40] 2.2 Fixed-Point Iteration [46] 2.3 The Newton-Raphson Method [56] 2.4 Error Analysis for Iterative Methods [70] 2.5 Accelerating Convergence [78] 2.6 Zeros of Polynomials and Muller’s Method [82] 2.7 Survey of Methods and Software [93] 3 Interpolation and Polynomial Approximation [95] 3.1 Interpolation and the Lagrange Polynomial [98] 3.2 Divided Differences [112] 3.3 Hermite Interpolation [123] 3.4 Cubic Spline Interpolation [130] 3.5 Parametric Curves [148] 3.6 Survey of Methods and Software [154] 4 Numerical Differentiation and Integration [156] 4.1 Numerical Differentiation [157] 4.2 Richardson’s Extrapolation [168] 4.3 Elements of Numerical Integration [174] 4.4 Composite Numerical Integration [184] 4.5 Adaptive Quadrature Methods [192] 4.6 Romberg Integration [199] 4.7 Gaussian Quadrature [205] 4.8 Multiple Integrals [211] 4.9 Improper Integrals [224] 4.10 Survey of Methods and Software [230] Initial-Value Problems for Ordinary Differential Equations [232] 5.1 Elementary Theory of Initial-Value Problems [234] 5.2 Euler’s Method [239] 5.3 Higher-Order Taylor Methods [248] 5.4 Runge-Kutta Methods [254] 5.5 Error Control and the Runge-Kutta-Fehlberg Method [263] 5.6 Multistep Methods [270] 5.7 Variable Step-Size Multistep Methods [282] 5.8 Extrapolation Methods [288] 5.9 Higher-Order Equations and Systems of Differential Equations [294] 5.10 Stability [304] 5.11 Stiff Differential Equations [314] 5.12 Survey of Methods and Software [321] Direct Methods for Solving Linear Systems [323] 6.1 Linear Systems of Equations [324] 6.2 Pivoting Strategies [338] 6.3 Linear Algebra and Matrix Inversion [345] 6.4 The Determinant of a Matrix [358] 6.5 Matrix Factorization [362] 6.6 Special Types of Matrices [371] 6.7 Survey of Methods and Software [386] Y Iterative Techniques in Matrix Algebra [389] 7 A Norms of Vectors and Matrices [390] 7.2 Eigenvalues and Eigenvectors [401] 7.3 Iterative Techniques for Solving Linear Systems [406] 1A Error Estimates and Iterative Refinement [424] 7.5 Survey of Methods and Software [434] Approximation Theory [435] 8.1 Discrete Least-Squares Approximation [436] 8.2 Orthogonal Polynomials and Least-Squares Approximation [449] 8.3 Chebyshev Polynomials and Economization of Power Series [459] 8.4 Rational Function Approximation [469] 8.5 Trigonometric Polynomial Approximation [480] 8.6 Fast Fourier Transforms [485] 8.7 Survey of Methods and Software [496] C) Approximating Eigenvalues [497] 9.1 Linear Algebra and Eigenvalues [498] 9.2 The Power Method [506] 9.3 Householder’s Method [523] 9.4 The QR Algorithm [530] 9.5 Survey of Methods and Software [541] 10 Numerical Solutions of Nonlinear Systems of Equations [543] 10.1 Fixed Points for Functions of Several Variables [544] 10.2 Newton’s Method [553] 10.3 Quasi-Newton Methods [560] 10.4 Steepest Descent Techniques [568] 10.5 Survey of Methods and Software [575] Boundary-Value Problems for Ordinary Differential Equations [577] 11.1 The Linear Shooting Method [578] 11.2 The Shooting Method for Nonlinear Problems [585] 11.3 Finite-Difference Methods for Linear Problems [592] 11.4 Finite-Difference Methods for Nonlinear Problems [598] 11.5 Rayleigh-Ritz Method [605] 11.6 Survey of Methods and Software [620] 12 Numerical Solutions to Partial-Differential Equations [622] 12.1 Elliptic Partial-Differential Equations [625] 12.2 Parabolic Partial-Differential Equations [635] 12.3 Hyperbolic Partial-Differential Equations [649] 12.4 An Introduction to the Finite-Element Method [657] 12.5 Survey of Methods and Software [672] Bibliography [675] Answers to Selected Exercises [685] Index [761]
| Item type | Home library | Call number | Materials specified | Status | Date due | Barcode | Course reserves |
|---|---|---|---|---|---|---|---|
Libros
|
Instituto de Matemática, CONICET-UNS | 65 B949 (Browse shelf) | Available | A-6794 |
Incluye referencias bibliográficas (p. 675-683) e índice.
1 Mathematical Preliminaries [1] --
1.1 Review of Calculus [2] --
1.2 Round-Off Errors and Computer Arithmetic [12] --
1.3 Algorithms and Convergence [24] --
1.4 Numerical Software [32] --
2 Solutions of Equations in One Variable [39] --
2.1 The Bisection Method [40] --
2.2 Fixed-Point Iteration [46] --
2.3 The Newton-Raphson Method [56] --
2.4 Error Analysis for Iterative Methods [70] --
2.5 Accelerating Convergence [78] --
2.6 Zeros of Polynomials and Muller’s Method [82] --
2.7 Survey of Methods and Software [93] --
3 Interpolation and Polynomial Approximation [95] --
3.1 Interpolation and the Lagrange Polynomial [98] --
3.2 Divided Differences [112] --
3.3 Hermite Interpolation [123] --
3.4 Cubic Spline Interpolation [130] --
3.5 Parametric Curves [148] --
3.6 Survey of Methods and Software [154] --
4 Numerical Differentiation and Integration [156] --
4.1 Numerical Differentiation [157] --
4.2 Richardson’s Extrapolation [168] --
4.3 Elements of Numerical Integration [174] --
4.4 Composite Numerical Integration [184] --
4.5 Adaptive Quadrature Methods [192] --
4.6 Romberg Integration [199] --
4.7 Gaussian Quadrature [205] --
4.8 Multiple Integrals [211] --
4.9 Improper Integrals [224] --
4.10 Survey of Methods and Software [230] --
Initial-Value Problems for Ordinary Differential Equations [232] --
5.1 Elementary Theory of Initial-Value Problems [234] --
5.2 Euler’s Method [239] --
5.3 Higher-Order Taylor Methods [248] --
5.4 Runge-Kutta Methods [254] --
5.5 Error Control and the Runge-Kutta-Fehlberg Method [263] --
5.6 Multistep Methods [270] --
5.7 Variable Step-Size Multistep Methods [282] --
5.8 Extrapolation Methods [288] --
5.9 Higher-Order Equations and Systems of Differential Equations [294] --
5.10 Stability [304] --
5.11 Stiff Differential Equations [314] --
5.12 Survey of Methods and Software [321] --
Direct Methods for Solving Linear Systems [323] --
6.1 Linear Systems of Equations [324] --
6.2 Pivoting Strategies [338] --
6.3 Linear Algebra and Matrix Inversion [345] --
6.4 The Determinant of a Matrix [358] --
6.5 Matrix Factorization [362] --
6.6 Special Types of Matrices [371] --
6.7 Survey of Methods and Software [386] --
Y Iterative Techniques in Matrix Algebra [389] --
7 A Norms of Vectors and Matrices [390] --
7.2 Eigenvalues and Eigenvectors [401] --
7.3 Iterative Techniques for Solving Linear Systems [406] --
1A Error Estimates and Iterative Refinement [424] --
7.5 Survey of Methods and Software [434] --
Approximation Theory [435] --
8.1 Discrete Least-Squares Approximation [436] --
8.2 Orthogonal Polynomials and Least-Squares Approximation [449] --
8.3 Chebyshev Polynomials and Economization of Power Series [459] --
8.4 Rational Function Approximation [469] --
8.5 Trigonometric Polynomial Approximation [480] --
8.6 Fast Fourier Transforms [485] --
8.7 Survey of Methods and Software [496] --
C) Approximating Eigenvalues [497] --
9.1 Linear Algebra and Eigenvalues [498] --
9.2 The Power Method [506] --
9.3 Householder’s Method [523] --
9.4 The QR Algorithm [530] --
9.5 Survey of Methods and Software [541] --
10 Numerical Solutions of Nonlinear Systems of Equations [543] --
10.1 Fixed Points for Functions of Several Variables [544] --
10.2 Newton’s Method [553] --
10.3 Quasi-Newton Methods [560] --
10.4 Steepest Descent Techniques [568] --
10.5 Survey of Methods and Software [575] --
Boundary-Value Problems for Ordinary Differential Equations [577] --
11.1 The Linear Shooting Method [578] --
11.2 The Shooting Method for Nonlinear Problems [585] --
11.3 Finite-Difference Methods for Linear Problems [592] --
11.4 Finite-Difference Methods for Nonlinear Problems [598] --
11.5 Rayleigh-Ritz Method [605] --
11.6 Survey of Methods and Software [620] --
12 Numerical Solutions to Partial-Differential Equations [622] --
12.1 Elliptic Partial-Differential Equations [625] --
12.2 Parabolic Partial-Differential Equations [635] --
12.3 Hyperbolic Partial-Differential Equations [649] --
12.4 An Introduction to the Finite-Element Method [657] --
12.5 Survey of Methods and Software [672] --
Bibliography [675] --
Answers to Selected Exercises [685] --
Index [761] --
MR, REVIEW #
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