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Reviewer name: Miloslav Znojil
Reviewer number: 9689
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)
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

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

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: