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A parallel method for solving pentadiagonal systems of linear equations

**
Ivan G. Ivanov and Chris Walshaw
**

### Abstract:

A new parallel approach for solving a pentadiagonal linear system is presented.
The parallel partition method for this system and the *TW* parallel partition
method on a chain of *P* processors are introduced and discussed. The result
of this algorithm is a reduced pentadiagonal linear system of order *P* - 2
compared with a system of order 2*P*-2 for the parallel partition method.
More importantly the new method involves only half the number of communications
startups than the parallel partition method (and other standard parallel
methods) and hence is a far more efficient parallel algorithm.

**Keywords.** parallel algorithm, linear system, pentadiagonal matrix,
block tridiagonal matrix

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Fri Aug 13 13:43:01 BST 2004