A parallel partition method for solving banded systems of linear equations. (English) Zbl 0599.65016

Meier, U.

Parallel Comput. 2, 33-43 (1985).

A partition method for solving systems of linear algebraic equations with banded nonsingular matrix is presented as a generalization of the partition method for tridiagonal systems by H. H. Wang [ACM Trans. Math. Software 7, 170-183 (1981; Zbl 0473.65010)]. A sufficient condition for the numerical stability of diagonally dominant matrices is proved. Operation counts for scalar and vector cases, and for parallel computers are given. Comparison aspects of the method with Gaussian elimination and the parallel cyclic reduction are presented together with examples of tri- and pentadiagonal systems implemented on the CRAY X-MP.

Reviewer: L.Bakule

MSC:

65F05	Direct numerical methods for linear systems and matrix inversion
15A23	Factorization of matrices
68N25	Theory of operating systems

Keywords:

banded matrices; partition method; numerical stability; diagonally dominant matrices; parallel computers; Comparison; Gaussian elimination; parallel cyclic reduction

Citations:

Zbl 0473.65010