Reviewer name:

Miloslav Znojil

Reviewer
number: 
9689 
Email:

znojil@ujf.cas.cz 
ZblNumber:

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, 3342
(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 twobytwo
blockdiagonalizing
rotations) and factorization (in the, combined
again, up and down
direction).
The details are inspiring and include the
reorderings 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  fillin
pattern. The real impact of these technical
ingredients is
illustrated and validated by a few tests.
Remarks to the editors:
