Parallel Gaussian elimination for banded matrix-a computational model

Author

Mani, V. ; Dattaguru, B. ; Balakrishnan, N. ; Ramamurthy, T.S.

Author_Institution

Dept. of Aerosp. Eng., Indian Inst. of Sci., Bangalore, India

fYear

1990

fDate

24-27 Sep 1990

Firstpage

170

Abstract

A parallel Gaussian elimination technique for the solution of a system of equations of the form Ax=C, where A is a banded matrix, is modeled as an acyclic directed graph. This graph is useful in the identification of parallel operations, the minimum absolute completion time for the solution process and the minimum number of processors required to solve it in minimum time. Hu´s (1961) level scheduling strategy is used for scheduling operations to processors. The absolute minimum completion time sets a limit on the speedup; it is dependent on the order of the A matrix and is independent of the bandwidth. The minimum number of processors required to complete the solution process is fixed by the bandwidth and is independent of the order of the A matrix. A method of incorporating communication aspects in between processors in four kinds of interconnections is also presented

Keywords

computation theory; matrix algebra; parallel algorithms; scheduling; acyclic directed graph; banded matrix; bandwidth; communication; completion time; computational model; interconnections; linear equations solution; parallel Gaussian elimination; processors; scheduling; task graph; Bandwidth; Computational modeling; Computer architecture; Concurrent computing; Equations; Finite element methods; Parallel algorithms; Parallel processing; Processor scheduling; Scientific computing;

fLanguage

English

Publisher

ieee

Conference_Titel

Computer and Communication Systems, 1990. IEEE TENCON'90., 1990 IEEE Region 10 Conference on

Print_ISBN

0-87942-556-3

Type

conf

DOI

10.1109/TENCON.1990.152591

Filename

152591