IJPAM: Volume 1, No. 1 (2002)
FOR PENTADIAGONAL LINEAR SYSTEMS

Kuwait University
P.O. Box 5969, Safat 13060, KUWAIT
Abstract.Classical elimination procedure is extended to uncouple
partitioned pentadiagonal linear systems for parallel processing of their
solution. In each block of equations, we need two sets of simultaneous
eliminations; each set consists of two usual forward eliminations and two
backward from across the succeeding block. While vertical fill-ins in the
last two columns of the block on the left pose no difficulty, the purpose of
the indicated eliminations is to move fill-ins in the last two rows
successively two columns to the right till they reach their destination in
the last two columns of each block. At the end of the elimination stage, we
reach a relatively small size block tridiagonal core system.
Once the core system is solved, the blocks of equations uncouple and the
uncoupled subsystems are solved in parallel by back substitution. We include
arithmetical operations counts for both serial and parallel implementations
of the presented algorithm and illustrate the working of the algorithm by an
example.
Received: January 20, 2002
AMS Subject Classification: 65F30, 15A06
Key Words and Phrases: linear systems, pentadiagonal, partitioning, elimination, parallel algorithm.
Source: International Journal of Pure and Applied Mathematics
ISSN: 1311-8080
Year: 2002
Volume: 1
Issue: 1