Abstract
Gaussian elimination with partial pivoting achieved by adding the pivot row to the kth row at step k, was introduced by Onaga and Takechi in 1986 as a means for reducing communications in parallel implementations. In this paper it is shown that the growth factor of this partial pivoting algorithm is bounded above by μn < 3n-1, as compared to 2n-1 for the standard partial pivoting. This bound μn, close to 3n-2, is attainable for a class of near-singular matrices. Moreover, for the same matrices the growth factor is small under partial pivoting.
Original language | English (US) |
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Pages (from-to) | 633-639 |
Number of pages | 7 |
Journal | BIT Numerical Mathematics |
Volume | 41 |
Issue number | 3 |
DOIs | |
State | Published - Sep 2001 |
Keywords
- Gaussian elimination
- Growth factor
- Parallel algorithm
- Stability
ASJC Scopus subject areas
- Software
- Computer Networks and Communications
- Computational Mathematics
- Applied Mathematics