Development of block and partitioned Neville elimination

Neville elimination is an elimination method which creates zeros in a colum n of a matrix by adding to each row an appropriate multiple of the previous one. This elimination procedure, alternative to Gaussian elimination, has proved to be useful when dealing with some special classes of matrices such as totally positive matrices. In this paper we analyze block and partition ed Neville elimination, necessary steps in order to adapt Neville eliminati on to many high performance computer architectures. (C) 1999 Academie des s ciences/Editions scientifiques et medicales Elsevier SAS.