General matrix-matrix multiplications with double-precision real and complex entries
(DGEMM and ZGEMM) in vendor-supplied BLAS libraries are best optimized for square …

We present two implementations of dense matrix multiplication based on two different non-
canonical array layouts: one based on a hypermatrix data structure (HM) where data …

Matrix computations lie at the heart of most scientific computational tasks. The solution of
linear systems of equations is a very frequent operation in many fields in science …

Dense linear algebra codes are often expressed and coded in terms of BLAS calls. This
approach, however, achieves suboptimal performance due to the overheads associated to …

Four routines called DPOTF3i, i= a, b, c, d, are presented. DPOTF3i are a novel type of level-
3 BLAS for use by BPF (B locked P acked F ormat) Cholesky factorization and LAPACK …

Some Linear Algebra Libraries use Level-2 routines during the factorization part of any
Level-3 block factorization algorithm. We discuss four Level-3 routines called DPOTF3i, i= a …

Efficient execution on processors with multiple cores requires the exploitation of parallelism
within the processor. For many dense linear algebra codes this, in turn, requires the efficient …

Using nonlinear array layouts in dense matrix operations Page 1 Using nonlinear array
layouts in dense matrix operations JR Herrero Introduction: A bottom-up approach …

This contribution describes a Square Block, SB, format for storing a banded symmetric
matrix. This is possible by rearranging “in place” LAPACK Band Layout to become a SB …

Abstract Some Linear Algebra Libraries use Level-2 routines during the factorization part of
any Level-3 block factorization algorithm. We discuss four Level-3 routines called DPOTF3 …