Average-case stability of Gaussian elimination
SIAM Journal on Matrix Analysis and Applications
Introduction to parallel computing: design and analysis of algorithms
Introduction to parallel computing: design and analysis of algorithms
Public international benchmarks for parallel computers: PARKBENCH committee: Report-1
Scientific Programming
Backward error analysis of Neville elimination
Applied Numerical Mathematics
Algorithmic Redistribution Methods for Block-Cyclic Decompositions
IEEE Transactions on Parallel and Distributed Systems
Block-Striped Partitioning and Neville Elimination
Euro-Par '99 Proceedings of the 5th International Euro-Par Conference on Parallel Processing
Performance of Various Computers Using Standard Linear Equations Software
Performance of Various Computers Using Standard Linear Equations Software
| Hi-index | 0.00 |
This paper presents a parallel algorithm to solve linear equation systems. This method, known as Neville elimination, is appropriate especially for the case of totally positive matrices (all its minors are non-negative). We discuss one common way to partition coefficient matrix among processors. In our mapping, called columwise block-cyclic-striped mapping, the matrix is divided into blocks of complete columns and these blocks are distributed among the processors in a cyclic way. The theoretic asymptotic estimation assures the speed-up to be k (being k the processor number); so the efficiency can take the value 1. Furthermore, in order to study the performance of the algorithm over a real machine (IBM SP2), some constants have been estimated. If such constants take these experimental values, then theoretic results are confirmed.