A Parallel Multi-threaded Solver for Symmetric Positive Definite Bordered-Band Linear Systems

We present a multi-threaded solver for symmetric positive de nite linear systems where the coe cient 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 e cient kernels from the Level-3 and Level-2 BLAS. The efciency of our approach is illustrated by numerical experiments.