Solution of Strictly Diagonal Dominant Tridiagonal Systems on Vector Computers

Abstract

. In this paper we propose the Overlapped Partitions Method (OPM) which is a new parallel solver for strictly diagonal dominant banded systems of equations. OPM is studied here for the case of tridiagonal systems of equations. OPM is compared with early terminated versions of the Cyclic Reduction and the Tricyclic Reduction methods on the vector computer Convex C-3480. Cyclic Reduction is a tridiagonal solver broadly used on vector and parallel computers. Tricyclic Reduction is a fairly new tridiagonal solver very well adapted to the architecture of vector computers. For the comparison of the three methods we build models of the algorithms and use these models to compare their execution times on the Convex C-3480. In the paper we also propose a new criterion for the early termination of TR. Key words. tridiagonal systems, vector processors, parallel numerical algorithms. AMS (MOS) subject classifications. 65F05, 65W05. Abreviated title: Tridiagonal systems on vector computers. 1. In..