A Feature Complete SPIKE Banded Algorithm and Solver
For users of banded linear solvers, this work makes the SPIKE algorithm more flexible and competitive, addressing long-standing limitations.
This paper enhances the SPIKE banded solver by removing the power-of-two core limitation, adding a transpose solve option, and introducing a pivoting recursive strategy. The new SPIKE-OpenMP package significantly outperforms other state-of-the-art banded solvers in performance and scalability.
New features and enhancements for the SPIKE banded solver are presented. Among all the SPIKE algorithm versions, we focus our attention on the recursive SPIKE technique which provides the best trade-off between generality and parallel efficiency, but was known for its lack of flexibility. Its application was essentially limited to power of two number of cores/processors. This limitation is successfully addressed in this paper. In addition, we present a new transpose solve option, a standard feature of most numerical solver libraries which has never been addressed by the SPIKE algorithm so far. A pivoting recursive SPIKE strategy is finally presented as an alternative to non-pivoting scheme for systems with large condition numbers. All these new enhancements participate to create a feature complete SPIKE algorithm and a new black-box SPIKE-OpenMP package that significantly outperforms the performance and scalability obtained with other state-of-the-art banded solvers.