Sparse Matrix TechnologySparse Matrix Technology presents the methods, concepts, ideas, and applications of sparse matrix technology. The text provides the fundamental methods, procedures, techniques, and applications of sparse matrix technology in software development. The book covers topics on storage schemes and computational techniques needed for sparse matrix technology; sparse matrix methods and algorithms for the direct solution of linear equations; and algorithms for different purposes connected with sparse matrix technology. Engineers, programmers, analysts, teachers, and students in the computer sciences will find the book interesting. |
Contents
| 1 | |
| 4 | |
Chapter 2 Linear Algebraic Equations | 38 |
Chapter 3 Numerical Errors in Gausss Elimination | 69 |
Symmetric Matrices | 94 |
General Matrices | 159 |
Chapter 6 Sparse Eigenanalysis | 196 |
Chapter 7 Sparse Matrix Algebra | 233 |
Chapter 8 Connectivity and Nodal Assembly | 271 |
Chapter 9 General Purpose Algorithms | 288 |
| 301 | |
| 313 | |
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Common terms and phrases
active submatrix adjacent array augmenting path band matrix belong calculated Chapter column indices computed connected consider convergence corresponding defined diagonal elements diagonal matrix digraph discussed in Section Duff edges efficient eigenproblem eigenvalues eigenvectors elementary matrices example fill fill-in final find finding finite element first Gauss elimination given matrix graph G graph of Fig integers inverse inverse iteration iteration labelled Lanczos algorithm level structure linear equations lower triangular method multiple switch nested dissection nonzeros of row number of nonzeros obtained off-diagonal nonzeros orthogonal partitioning performed permuted matrix pointers problem procedure profile representation resulting matrix rooted row-wise format rows and columns shown in Fig solved sparse matrix sparse matrix technology sparsity stack starting vertex storage scheme stored strong component submatrix sufficiently symbolic symmetric matrix symmetric positive definite tree arcs triangular factorization tridiagonal undirected graph unit diagonal unsymmetric upper triangular vertex vertices zeros