Numerical analysis : mathematics of scientific computing / David Kincaid and Ward Cheney.
Editor: Pacific Grove, Calif. : Brooks/Cole, c1991Descripción: viii, 690 p. : il. ; 25 cmISBN: 0534130143Tema(s): Numerical analysisOtra clasificación: 65-01Chapter 1. MATHEMATICAL PRELIMINARIES [1] 1.1 Basic Concepts and Taylor’s Theorem [1] 1.2 Orders of Convergence and Additional Basic Concepts [9] *1.3 Difference Equations [20] Chapter 2. COMPUTER ARITHMETIC [28] 2.1 Floating-Point Numbers and Roundoff Errors [28] 2.2 Absolute and Relative Errors; Loss of Significance [41] 2.3 Stable and Unstable Computations; Conditioning [48] Chapter 3. SOLUTION OF NONLINEAR EQUATIONS [57] 3.1 Bisection Method [57] 3.2 Newton’s Method [64] 3.3 Secant Method [75] *3.4 Fixed Points and Functional Iteration [80] *3.5 Computing Zeros of Polynomials [88] *3.6 Homotopy and Continuation Methods [108] Chapter 4. SOLVING SYSTEMS OF LINEAR EQUATIONS [116] 4.1 Matrix Algebra [117] 4.2 The LU and Cholesky Factorizations [126] 4.3 Pivoting and Constructing an Algorithm [139] 4.4 Norms and the Analysis of Errors [161] 4.5 Neumann Series and Iterative Refinement [171] *4.6 Solution of Equations by Iterative Methods [181] *4.7 Steepest Descent and Conjugate Gradient Methods [204] *4.8 Analysis of Roundoff Error in the Gaussian Algorithm [219] Chapter 5. SELECTED TOPICS IN NUMERICAL LINEAR ALGEBRA [226] 5.1 Matrix Eigenvalue Problem: Power Method [226] 5.2 Schur’s and Gershgorin’s Theorems [237] *5.3 Orthogonal Factorizations and Least-Squares Problems [245] *5.4 Singular-Value Decomposition and Pseudoinverses [258] *5.5 The QR-Algorithm of Francis for the Eigenvalue Problem [269] Chapter 6. APPROXIMATING FUNCTIONS [278] 6.1 Polynomial Interpolation [278] 6.2 Divided Differences [296] 6.3 Hermite Interpolation [305] 6.4 Spline Interpolation [315] *6.5 The B-Splines: Basic Theory [333] *6.6 The B-Splines: Applications [343] 6.7 Taylor Series [354] *6.8 Best Approximation: Least-Squares Theory [359] *6.9 Best Approximation: Chebyshev Theory [370] *6.10 Interpolation in Higher Dimensions [385] *6.11 Continued Fractions [403] *6.12 Trigonometric Interpolation and the Fast Fourier Transform [409] 6.13 Adaptive Approximation [424] Chapter 7. NUMERICAL DIFFERENTIATION AND INTEGRATION [430] 7.1 Numerical Differentiation and Richardson Extrapolation [430] 7.2 Numerical Integration Based on Interpolation [443] 7.3 Gaussian Quadrature [456] 7.4 Romberg Integration [465] 7.5 Adaptive Quadrature [471] *7.6 Sard’s Theory of Approximating Functionals [477] *7.7 Bernoulli Polynomials and the Euler-Maclaurin Formula [481] Chapter 8. NUMERICAL SOLUTION OF ORDINARY DIFFERENTIAL EQUATIONS [486] 8.1 The Existence and Uniqueness of Solutions [486] 8.2 Taylor-Series Method [491] 8.3 Runge-Kutta Methods [499] 8.4 Multi-Step Methods [508] *8.5 Local and Global Errors; Stability [516] 8.6 Systems and Higher-Order Ordinary Differential Equations [524] *8.7 Boundary-Value Problems [531] 8.8 Boundary-Value Problems: Shooting Methods [540] 8.9 Boundary-Value Problems: Finite-Difference Methods [547] *8.10 Boundary-Value Problems: Collocation [551] *8.11 Linear Differential Equations [555] 8.12 Stiff Equations [566] Chapter 9. NUMERICAL SOLUTION OF PARTIAL DIFFERENTIAL EQUATIONS [572] 9.1 Parabolic Equations: Explicit Methods [572] 9.2 Parabolic Equations: Implicit Methods [580] 9.3 Problems Without Time Dependence: Finite-Difference Methods [586] *9.4 Problems Without Time Dependence: Galerkin and Ritz Methods [591] *9.5 First-Order Partial Differential Equations; Characteristic Curves [598] *9.6 Quasi-Linear Second-Order Equations; Characteristics [606] *9.7 Other Methods for Hyperbolic Problems [616] 9.8 Multigrid Method [622] *9.9 Fast Methods for Poisson’s Equation [631] Chapter 10. LINEAR PROGRAMMING AND RELATED TOPICS [636] *10.1 Convexity and Linear Inequalities [636] * 10.2 Linear Inequalities [642] 10.3 Linear Programming [647] 10.4 The Simplex Algorithm [652] ANSWERS AND HINTS [662] BIBLIOGRAPHY [667] INDEX [683]
| Item type | Home library | Shelving location | Call number | Materials specified | Copy number | Status | Date due | Barcode | Course reserves |
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Instituto de Matemática, CONICET-UNS | Libros ordenados por tema | 65 K51 (Browse shelf) | Available | A-6791 |
ELEMENTOS DE MÉTODOS NUMÉRICOS |
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Instituto de Matemática, CONICET-UNS | Libros ordenados por tema | 65 K51 (Browse shelf) | Ej. 2 | Available | A-6875 |
Incluye referencias bibliográficas (p. 667-682) e índice.
Chapter 1. MATHEMATICAL PRELIMINARIES [1] --
1.1 Basic Concepts and Taylor’s Theorem [1] --
1.2 Orders of Convergence and Additional Basic Concepts [9] --
*1.3 Difference Equations [20] --
Chapter 2. COMPUTER ARITHMETIC [28] --
2.1 Floating-Point Numbers and Roundoff Errors [28] --
2.2 Absolute and Relative Errors; Loss of Significance [41] --
2.3 Stable and Unstable Computations; Conditioning [48] --
Chapter 3. SOLUTION OF NONLINEAR EQUATIONS [57] --
3.1 Bisection Method [57] --
3.2 Newton’s Method [64] --
3.3 Secant Method [75] --
*3.4 Fixed Points and Functional Iteration [80] --
*3.5 Computing Zeros of Polynomials [88] --
*3.6 Homotopy and Continuation Methods [108] --
Chapter 4. SOLVING SYSTEMS OF LINEAR EQUATIONS [116] --
4.1 Matrix Algebra [117] --
4.2 The LU and Cholesky Factorizations [126] --
4.3 Pivoting and Constructing an Algorithm [139] --
4.4 Norms and the Analysis of Errors [161] --
4.5 Neumann Series and Iterative Refinement [171] --
*4.6 Solution of Equations by Iterative Methods [181] --
*4.7 Steepest Descent and Conjugate Gradient Methods [204] --
*4.8 Analysis of Roundoff Error in the Gaussian Algorithm [219] --
Chapter 5. SELECTED TOPICS IN NUMERICAL LINEAR ALGEBRA [226] --
5.1 Matrix Eigenvalue Problem: Power Method [226] --
5.2 Schur’s and Gershgorin’s Theorems [237] --
*5.3 Orthogonal Factorizations and Least-Squares Problems [245] --
*5.4 Singular-Value Decomposition and Pseudoinverses [258] --
*5.5 The QR-Algorithm of Francis for the Eigenvalue Problem [269] --
Chapter 6. APPROXIMATING FUNCTIONS [278] --
6.1 Polynomial Interpolation [278] --
6.2 Divided Differences [296] --
6.3 Hermite Interpolation [305] --
6.4 Spline Interpolation [315] --
*6.5 The B-Splines: Basic Theory [333] --
*6.6 The B-Splines: Applications [343] --
6.7 Taylor Series [354] --
*6.8 Best Approximation: Least-Squares Theory [359] --
*6.9 Best Approximation: Chebyshev Theory [370] --
*6.10 Interpolation in Higher Dimensions [385] --
*6.11 Continued Fractions [403] --
*6.12 Trigonometric Interpolation and the Fast Fourier Transform [409] --
6.13 Adaptive Approximation [424] --
Chapter 7. NUMERICAL DIFFERENTIATION AND INTEGRATION [430] --
7.1 Numerical Differentiation and Richardson Extrapolation [430] --
7.2 Numerical Integration Based on Interpolation [443] --
7.3 Gaussian Quadrature [456] --
7.4 Romberg Integration [465] --
7.5 Adaptive Quadrature [471] --
*7.6 Sard’s Theory of Approximating Functionals [477] --
*7.7 Bernoulli Polynomials and the Euler-Maclaurin Formula [481] --
Chapter 8. NUMERICAL SOLUTION OF ORDINARY DIFFERENTIAL EQUATIONS [486] --
8.1 The Existence and Uniqueness of Solutions [486] --
8.2 Taylor-Series Method [491] --
8.3 Runge-Kutta Methods [499] --
8.4 Multi-Step Methods [508] --
*8.5 Local and Global Errors; Stability [516] --
8.6 Systems and Higher-Order Ordinary Differential Equations [524] --
*8.7 Boundary-Value Problems [531] --
8.8 Boundary-Value Problems: Shooting Methods [540] --
8.9 Boundary-Value Problems: Finite-Difference Methods [547] --
*8.10 Boundary-Value Problems: Collocation [551] --
*8.11 Linear Differential Equations [555] --
8.12 Stiff Equations [566] --
Chapter 9. NUMERICAL SOLUTION OF PARTIAL DIFFERENTIAL EQUATIONS [572] --
9.1 Parabolic Equations: Explicit Methods [572] --
9.2 Parabolic Equations: Implicit Methods [580] --
9.3 Problems Without Time Dependence: Finite-Difference Methods [586] --
*9.4 Problems Without Time Dependence: Galerkin and Ritz Methods [591] --
*9.5 First-Order Partial Differential Equations; Characteristic Curves [598] --
*9.6 Quasi-Linear Second-Order Equations; Characteristics [606] --
*9.7 Other Methods for Hyperbolic Problems [616] --
9.8 Multigrid Method [622] --
*9.9 Fast Methods for Poisson’s Equation [631] --
Chapter 10. LINEAR PROGRAMMING AND RELATED TOPICS [636] --
*10.1 Convexity and Linear Inequalities [636] --
* 10.2 Linear Inequalities [642] --
10.3 Linear Programming [647] --
10.4 The Simplex Algorithm [652] --
ANSWERS AND HINTS [662] --
BIBLIOGRAPHY [667] --
INDEX [683] --
MR, 92c:65002
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