Elementary numerical analysis ; an algorithmic approach / [by] S. D. Conte [and] Carl de Boor.
Series International series in pure and applied mathematicsEditor: New York : McGraw-Hill, [1972]Edición: 2nd edDescripción: x, 396 p. : il. ; 23 cmISBN: 0070124464Tema(s): Numerical analysis -- Data processingOtra clasificación: 65-011• Number Systems and Errors I LI The Representation of Integers [1] 1.2 The Representation of Fractions [4] 1.3 Floating-point Arithmetic [7] 1.4 Error Propagation; Significance Errors and Instability [10] 1.5 Computational Methods for Error Estimation [15] 1.6 Some Comments on Convergence of Sequences [17] 1.7 Some Mathematical Preliminaries [21] 2. The Solution of Nonlinear Equations [27] 2.1 A Survey of Iterative Methods [28] 2.2 FORTRAN Programs for Some Iterative Methods [35] 2.3 Fixed-point Iteration [44] 2.4 Convergence Acceleration for Fixed-point Iteration [50] 2.5 Quadratic Convergence and Newton’s Method [57] 2.6 Polynomial Equations: Real Roots [66] 2.7 Complex Roots and Muller’s Method [74] 2.8 Simultaneous Nonlinear Equations [84] 3. Matrices and Systems of Linear Equations [91] 3.1 Properties of Matrices [91] 3.2 The Solution of Linear Systems by Elimination [110] 3.3 The Pivoting Strategy [123] 3.4 The Triangular Factorization and Calculation of the Inverse [127] 3.5 Compact Schemes [137] 3.6 Error and Residual of an Approximate Solution; Norms [142] 3.7 The Condition Number and Iterative Improvement [150] 3.8 Iterative Methods [157] 3.9 Eigenvalues and the Convergence of Fixed-point Iteration [170] 3.10 Determinants [180] 3.11 The Eigenvalue Problem [184] 4. Interpolation and Approximation [191] 4.1 The Interpolating Polynomial: Lagrange Form [191] 4.2 The Interpolating Polynomial: Newton Form [195] 4.3 The Divided-difference Table [201] 4.4 The Error of the Interpolating Polynomial [210] 4.5 Interpolation in a Function Table Based on Equally Spaced Points [213] 4.6 The Divided Difference as a Function of Its Arguments and Osculatory Interpolation [221] 4.7 The Case for Piecewise-polynomial Interpolation [230] *4.8 Piecewise-cubic Interpolation [233] 4.9 Data Fitting [241] *4.10 Orthogonal Polynomials [246] *4.11 Least-squares Approximation by Polynomials [255] *4.12 Chebyshev Economization [265] 5. Differentiation and Integration [274] 5.1 Numerical Differentiation [275] 5.2 Numerical Integration: Some Basic Rules [284] 5.3 Numerical Integration: Composite Rules [290] 5.4 Numerical Integration: Gaussian Rules [299] 5.5 Extrapolation to the Limit; Romberg Integration [307] 6. The Solution of Differential Equations [319] 6.1 Mathematical Preliminaries [320] 6.2 Simple Difference Equations [322] 6.3 Numerical Integration by Taylor Series [327] 6.4 Error Estimates and Convergence of Euler’s Method [332] 6.5 Runge-Kutta Methods [336] 6.6 Multistep Formulas [340] 6.7 Predictor-Corrector Methods [346] 6.8 The Adams-Moulton Method [350] 6.9 Stability of Numerical Methods [357] 6.10 Round-off-error Propagation [361] 6.11 Systems of Differential Equations [365] 7. Boundary-value Problems in Ordinary Differential Equations [373] 7.1 Finite-difference Methods: Second-order Equations [374] 7.2 Finite-difference Methods: Fourth-order Equations [379] 7.3 Shooting Methods [382]
| Item type | Home library | Call number | Materials specified | Status | Date due | Barcode | Course reserves |
|---|---|---|---|---|---|---|---|
Libros
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Instituto de Matemática, CONICET-UNS | 65 C761 (Browse shelf) | Available | A-4810 |
1• Number Systems and Errors I --
LI The Representation of Integers [1] --
1.2 The Representation of Fractions [4] --
1.3 Floating-point Arithmetic [7] --
1.4 Error Propagation; Significance Errors and Instability [10] --
1.5 Computational Methods for Error Estimation [15] --
1.6 Some Comments on Convergence of Sequences [17] --
1.7 Some Mathematical Preliminaries [21] --
2. The Solution of Nonlinear Equations [27] --
2.1 A Survey of Iterative Methods [28] --
2.2 FORTRAN Programs for Some Iterative Methods [35] --
2.3 Fixed-point Iteration [44] --
2.4 Convergence Acceleration for Fixed-point Iteration [50] --
2.5 Quadratic Convergence and Newton’s Method [57] --
2.6 Polynomial Equations: Real Roots [66] --
2.7 Complex Roots and Muller’s Method [74] --
2.8 Simultaneous Nonlinear Equations [84] --
3. Matrices and Systems of Linear Equations [91] --
3.1 Properties of Matrices [91] --
3.2 The Solution of Linear Systems by Elimination [110] --
3.3 The Pivoting Strategy [123] --
3.4 The Triangular Factorization and Calculation of the Inverse [127] --
3.5 Compact Schemes [137] --
3.6 Error and Residual of an Approximate Solution; Norms [142] --
3.7 The Condition Number and Iterative Improvement [150] --
3.8 Iterative Methods [157] --
3.9 Eigenvalues and the Convergence of Fixed-point Iteration [170] --
3.10 Determinants [180] --
3.11 The Eigenvalue Problem [184] --
4. Interpolation and Approximation [191] --
4.1 The Interpolating Polynomial: Lagrange Form [191] --
4.2 The Interpolating Polynomial: Newton Form [195] --
4.3 The Divided-difference Table [201] --
4.4 The Error of the Interpolating Polynomial [210] --
4.5 Interpolation in a Function Table Based on Equally Spaced Points [213] --
4.6 The Divided Difference as a Function of Its Arguments and Osculatory Interpolation [221] --
4.7 The Case for Piecewise-polynomial Interpolation [230] --
*4.8 Piecewise-cubic Interpolation [233] --
4.9 Data Fitting [241] --
*4.10 Orthogonal Polynomials [246] --
*4.11 Least-squares Approximation by Polynomials [255] --
*4.12 Chebyshev Economization [265] --
5. Differentiation and Integration [274] --
5.1 Numerical Differentiation [275] --
5.2 Numerical Integration: Some Basic Rules [284] --
5.3 Numerical Integration: Composite Rules [290] --
5.4 Numerical Integration: Gaussian Rules [299] --
5.5 Extrapolation to the Limit; Romberg Integration [307] --
6. The Solution of Differential Equations [319] --
6.1 Mathematical Preliminaries [320] --
6.2 Simple Difference Equations [322] --
6.3 Numerical Integration by Taylor Series [327] --
6.4 Error Estimates and Convergence of Euler’s Method [332] --
6.5 Runge-Kutta Methods [336] --
6.6 Multistep Formulas [340] --
6.7 Predictor-Corrector Methods [346] --
6.8 The Adams-Moulton Method [350] --
6.9 Stability of Numerical Methods [357] --
6.10 Round-off-error Propagation [361] --
6.11 Systems of Differential Equations [365] --
7. Boundary-value Problems in Ordinary Differential Equations [373] --
7.1 Finite-difference Methods: Second-order Equations [374] --
7.2 Finite-difference Methods: Fourth-order Equations [379] --
7.3 Shooting Methods [382] --
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