A parallel multi-threaded solver for symmetric positive definite Bordered-Band linear systems

Abstract

We present a multi-threaded solver for symmetric positive definite linear systems where the coefficient matrix of the problem features a bordered-band non-zero pattern. The algorithms that implement this approach heavily rely on a compact storage format, tailored for this type of matrices, that reduces the memory requirements, produces a regular data access pattern, and allows to cast the bulk of the computations in terms of efficient kernels from the Level-3 and Level-2 BLAS. The efficiency of our approach is illustrated by numerical experiments.