Matrix ComputationsRevised 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 |
8 | 9 |
Matrix Analysis | 48 |
General Linear Systems | 87 |
Positive Definite Systems | 133 |
4 | 147 |
5 | 183 |
1 | 195 |
7 | 375 |
The Symmetric Eigenvalue Problem | 391 |
9 | 468 |
Applications to | 490 |
Arnoldi and Unsymmetric Lanczos | 499 |
Iterative Methods for Linear Systems | 508 |
Functions of Matrices | 555 |
Special Topics | 579 |
2 | 218 |
3 | 236 |
4 | 248 |
7 | 256 |
5 | 260 |
Parallel Matrix Computations | 275 |
7 | 303 |
4 | 341 |
6 | 343 |
2 | 590 |
206 | 600 |
4 | 601 |
ModifiedStructured Eigenproblems | 621 |
275 | 647 |
308 | 666 |
391 | 676 |
Other editions - View all
Common terms and phrases
1:n end ACM Trans Appl Applic arithmetic Band bidiagonal block matrix Bounds Cholesky factorization column Comp Condition Estimation Condition Numbers Conjugate Gradient Convergence defined diagonal dot product Eigenproblem Eigenvalue Problem eigenvectors end end entries example floating point flops following algorithm G.H. Golub G.W. Stewart Gaussian elimination gaxpy given Householder inverse Iterative Methods J.H. Wilkinson Jacobi Lanczos Algorithm LAPACK Least Squares Problems Linear Algebra Linear Equations Linear Systems lower triangular LU factorization Math Matrix Anal Matrix Computations matrix multiplication N.J. Higham nonsingular norm Numer obtain orthogonal orthogonal matrix outer product Parallel Computing permutation Perturbation processor QR Algorithm QR factorization rank(A References for Sec Rmxn Rnxn roundoff saxpy Schur decomposition Show SIAM Review Singular Value Decomposition solution solve Sparse Sparse Matrix Stat subspace Suppose symmetric positive definite Theorem Toeplitz transformations triangular system tridiagonal update upper Hessenberg upper triangular vector zero