数值分析（英文版.第3版）[按需印刷]

.4.1 matrix algebra
4.2 lu and cholesky factorizations
4.3 pivoting and constructing an algorithm
4.4 norms and the analysis of errors
4.5 neumann series and iterative refinement
4.6 solution of equations by iterative methods
4.7 steepest descent and conjugate gradient methods
4.8 analysis of roundoff error in the gaussian algorithm
5 selected topics in numerical linear algebra
5.0 review of basic concepts
5.1 matrix eigenvalue problem: power method
5.2 schur's and cershgorin's theorems
5.3 orthogonal factorizations and least-squares problems
5.4 singular-value decomposition and pseudoinverses
5.5 qr-algorithm of francis for the eigenvalue problem
6 approximating functions
6.0 introduction
6.1 polynomial interpolation
6.2 divided differences
6.3 hermite interpolation
6.4 spline interpolation
6.5 b-splines: basic theory
6.6 b-splines: applications
6.7 taylor series
6.8 best approximation: least-squares theory
6.9 best approximation: chebyshev theory
6.1o interpolatlon in higher dimensions
6.11 continued fractions
6.12 trigonometric interpolation
6.13 fast fourier transform
6.14 adaptive approximation
7 numerical differentiation and
7.1 numerical differentiation and
7.2 numerical integration based on
7.3 gaussian quadrature
7.4 romberg integration
7.5 adaptive quadrature
7.6 sard's theory of approximating functionals
7.7 bernoulli polynomials and the euler-maclaurin formula
8 numeriral solution ot ordinary
differential equations
8.0 introduction
8.1 the existence and uniqueness of solutions
8.2 taylor-series method
8.3 runge-kutta methods
8.4 multistep methods
8.5 local and global errors: stability
8.6 systems and higher-order ordinary differential equations
8.7 boundary-value problems
8.8 boundary-value problems: shooting methods
8.9 boundary-value problems: finite-differences
8.1 0 boundary-value problems: collocation
8.1 1 linear differential equations
8.1 2 stiff equations
9 numetical selution of partial differential equations
9.0 introduction
9.1 parabolic equations: explicit methods
9.2 parabolic equations: implicit methods
9.3 problems without without time dependence: finite-differences
9.4 problems without without time dependence: galerkin methods
9.5 first-order partial differential equations: characteristics
9.6 quasilinear second-order equations: characteristics
9.7 other methods for hyperbolic problems
9.8 multigrid method
9.9 fast methods for poisson's equation
10 linear programming and related topics
10.1 convexity and linear inequalities
10.2 linear inequalities
10.3 linear programming
10.4 the simplex algorithm
11 oytimization
11.0 introdudion
11.1 one-variable case
11.2 descent methods
11.3 analysis of quadratic objective functions
11.4 quadratic-fitting algorithms
11.5 nelder-meade algorithm
11.6 simulated annealing
11.7 cenetic algorithms
11.8 convex programming
11.9 constrained minimization
11.10 pareto optimization
appendix a an overview of mathematical software
bibliography
index