Gaussian-elimination-based algorithm for solving linear equations on mesh-connected processors

Author

Murthy, K.N.B. ; Murthy, C.S.R.

Author_Institution

Dept. of Electr. Eng., Malnad Coll. of Eng., Hassan, India

Volume

143

Issue

6

fYear

1996

fDate

11/1/1996 12:00:00 AM

Firstpage

407

Lastpage

412

Abstract

The problem of solving a system of N linear equations on a mesh-connected multiprocessor structure is considered. The solution to the problem is obtained by using a Gaussian-elimination-based algorithm called `successive Gaussian elimination´. The new algorithm does not contain a separate backsubstitution phase. A two-dimensional array of N×(N+1) processors is employed to obtain the solution in (5N-log N-4) time steps. This scheme eliminates the use of two processor structures in conjunction, one for triangulation and the other for backsubstitution, for producing the complete solution using the existing Gaussian elimination algorithm. Most importantly, the new algorithm supports pairwise pivoting to assure numerical stability. The proposed processor-array structure is amenable for VLSI implementation as identical processors with only simple and regular interconnections are required

Keywords

VLSI; computational complexity; linear algebra; mathematics computing; multiprocessing systems; numerical stability; parallel algorithms; systolic arrays; Gaussian-elimination-based algorithm; VLSI; backsubstitution phase; computation time; linear equation solving; mesh-connected multiprocessor structure; numerical stability; pairwise pivoting; successive Gaussian elimination; systolic arrays; triangulation; two-dimensional array;

fLanguage

English

Journal_Title

Computers and Digital Techniques, IEE Proceedings -

Publisher

iet

ISSN

1350-2387

Type

jour

DOI

10.1049/ip-cdt:19960562

Filename

556712