A Columnwise Block Striping in Neville Elimination

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.