A Feature Complete SPIKE Banded Algorithm and Solver

TL;DR

This paper enhances the recursive SPIKE banded solver by addressing its flexibility limitations, adding new features like transpose solve and pivoting strategies, resulting in a more complete and scalable solver package.

Contribution

It introduces a feature complete SPIKE algorithm with improved flexibility, including transpose solve and pivoting, and presents a high-performance SPIKE-OpenMP package.

Findings

Outperforms state-of-the-art banded solvers in performance and scalability.

Addresses limitations of previous SPIKE versions, including core number restrictions.

Provides a flexible, black-box solver with new features like pivoting and transpose solve.

Abstract

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.