| Reviewer name: | Miloslav Znojil |
| Reviewer number: | 9689 |
| Email: | znojil@ujf.cas.cz |
| Zbl-Number: | DE01487273X |
| Author(s): | Chen, P.; Runesha, H.; Nguyen, D. T.; Tong, P.; Chang, T. Y. P.; |
| Shorttitle: | Sparse algorithms for indefinite systems of linear equations |
| Source: | Comput. Mech. 25, No. 1, 33-42 (2000) |
| Classification: | |
| Primary Classification: | 65F50 65F50 - Sparse matrices |
| Secondary Classification: | 65F05 65F05 - Direct methods
for linear systems and matrix inversion |
| Keywords: | sparse systems of linear equations; not positive definite; factorization algorithm; pivoting 2 x 2 strategy |
| Review: There exists a number of Fortran codes for the systems of linear equations which are either sparse or do not have a positive definite matrix. Perversely, many practical applications call for a coincidence of both these features. The paper tries to meet the need and offers a new computational strategy. With emphasis on the efficiency (in both the accuracy and economy sense) and robust generality, a detailed proposal is based on a combined pivoting (mediated by a two-by-two block-diagonalizing rotations) and factorization (in the, combined again, up and down direction). The details are inspiring and include the re-orderings and simultaneity of the symbolic and numerical factorizations. Together with the restarts of memory arrangements they are designed to minimize the complexity of the -- variable -- fill-in pattern. The real impact of these technical ingredients is illustrated and validated by a few tests. Remarks to the editors: |
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