A parallel Cholesky factorization routine with a new version of PB-BLAS

PB-BLAS (Parallel Block Basic linear Algebra Subprograms) is the first parallel implementation of BLAS, whose data are decomposed based on a block cyclic data distribution. It is functionally an extended subset of the Level 2 and 3 BLAS for distributed-memory systems. The authors present a new modified version of PB-BLAS, which eliminated the positional restrictions of the data matrices from the old version. And it is more efficient in memory space management as well as in performance for PB-BLAS routines which handle a triangular, symmetric, or Hermitian matrix. The paper outlines PB-BLAS and ScaLAPACK, which is a library of high performance linear algebra routines for distributed-memory computers. And it describes a parallel Cholesky factorization routine, and shows the performance with the old and the new version of PB-BLAS on the Intel Paragon computer.