Matrix Iterative AnalysisSpringer Science & Business Media, 1999. 11. 17. - 358페이지 This book is a revised version of the first edition, regarded as a classic in its field. In some places, newer research results have been incorporated in the revision, and in other places, new material has been added to the chapters in the form of additional up-to-date references and some recent theorems to give readers some new directions to pursue. |
목차
Matrix Properties and Concepts | 1 |
SemiIterative Methods | 5 |
1 | 31 |
22 | 37 |
Basic Iterative Methods and Comparison Theorems | 63 |
Successive Overrelaxation Iterative Methods | 111 |
Derivation and Solution of Elliptic Difference Equations | 183 |
AlternatingDirection Implicit Iterative Methods | 235 |
Matrix Methods for Parabolic Partial Differential Equa | 275 |
Estimation of Acceleration Parameters | 313 |
A Appendix | 329 |
| 356 | |
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ai,i ai,j asymptotic rates bi,j Chebyshev semi-iterative method completes the proof components computation consider consistently ordered Corollary cyclic matrix cyclic of index defined derived diagonal entries diagonal matrix diagonal submatrices difference approximations directed graph eigenvalues eigenvector error vectors Exer follows function Gauss-Seidel iterative method Gauss-Seidel matrix H₁ and V₁ Hermitian matrix inequality initial vector irreducibly diagonally dominant Jacobi iterative method L₁ Lemma M-matrix matrix equation matrix norms matrix of index mesh points n×n complex matrix n×n matrix nonnegative irreducible nonnegative matrices nonsingular nonzero normal form overrelaxation iterative method p(Lw partial differential equations partitioned permutation matrix point Gauss-Seidel iterative point Jacobi matrix point successive overrelaxation polynomial positive definite positive integer primitive prove rates of convergence real numbers regular splitting Sect spectral norm spectral radius Stieltjes matrix successive overrelaxation iterative symmetric Theorem 3.8 tridiagonal Varga weakly cyclic zero