SPIKE As A Polyalgorithmic Banded Linear System Solver
Despite being logically divided into two stages, computationally, the SPIKE algorithm comprises three stages:
- factorizing the diagonal blocks,
- computing the spikes,
- solving the reduced system.
Each of these stages can be accomplished in several ways, allowing a multitude of variants. Two notable variants are the recursive SPIKE algorithm for non-diagonally-dominant cases and the truncated SPIKE algorithm for diagonally-dominant cases. Depending on the variant, a system can be solved either exactly or approximately. In the latter case, SPIKE is used as a preconditioner for iterative schemes like Krylov subspace methods and iterative refinement.
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