Research directions in sparse matrix computations. (English) Zbl 0595.65025

Duff, Iain S.

Studies in numerical analysis, MAA Stud. Math. 24, 83-139 (1984).

Some of the techniques used in the solution of sparse linear equations are described and areas of future research are pointed out. The author has concentrated on the solution of linear equations by direct methods. Gaussian elimination for sparse matrices is reviewed and it is shown that vast gains result from pivoting for sparsity. Methods taking advantage of structure of sparse systems are summarized. Some hybrid techniques that combine classical iterative methods with new direct methods are given. The author concludes with a list of sparse matrix software and suggestions for further reading.

Reviewer: R. P. Tewarson (Stony Brook)

MSC:

65F05	Direct numerical methods for linear systems and matrix inversion
65F10	Iterative numerical methods for linear systems
15-04	Software, source code, etc. for problems pertaining to linear algebra

Keywords:

sparse linear equations; Gaussian elimination; pivoting; hybrid techniques; sparse matrix software