Matrix ComputationsJHU Press, 1996 M10 15 - 694 pages Revised and updated, the third edition of Golub and Van Loan's classic text in computer science provides essential information about the mathematical background and algorithmic skills required for the production of numerical software. This new edition includes thoroughly revised chapters on matrix multiplication problems and parallel matrix computations, expanded treatment of CS decomposition, an updated overview of floating point arithmetic, a more accurate rendition of the modified Gram-Schmidt process, and new material devoted to GMRES, QMR, and other methods designed to handle the sparse unsymmetric linear system problem. |
Contents
Matrix Multiplication Problems | 1 |
Matrix Analysis | 48 |
General Linear Systems | 87 |
Special Linear Systems | 133 |
Orthogonalization and Least Squares | 206 |
Parallel Matrix Computations | 275 |
The Unsymmetric Eigenvalue Problem | 308 |
The Symmetric Eigenvalue Problem | 391 |
Lanczos Methods | 470 |
Iterative Methods for Linear Systems | 508 |
Functions of Matrices | 555 |
Special Topics | 579 |
| 637 | |
| 687 | |
Other editions - View all
Common terms and phrases
Analysis Appl Applic Assume bidiagonal block block matrix Cholesky factorization column Comp Conjugate Gradient convergence defined diagonal discussed Eigenproblem Eigenvalue Problem eigenvectors end end entries error example floating point flops following algorithm G.H. Golub G.W. Stewart Gaussian elimination gaxpy Givens rotations Hessenberg matrix Householder inverse IRmxn IRnxn Iterative Methods Jacobi Lanczos algorithm LAPACK Least Squares Problems Linear Algebra Linear Systems lower triangular LS problem LU factorization Math Matrix Anal Matrix Computations matrix multiplication minimize nonsingular norm Numer obtain orthogonal matrix outer product overwrites Parallel Computing permutation Perturbation pivoting polynomial processor Proof QR algorithm QR factorization rank(A References for Sec Rnxn roundoff Schur decomposition Show SIAM Singular Value Decomposition solution solve Sparse Sparse Matrix Suppose Symmetric Matrices symmetric positive definite Theorem Toeplitz transformations tridiagonal tridiagonal matrix update upper Hessenberg upper triangular vector zero λη