A Direct Projection Method for Sparse Linear Systems

Abstract

An oblique projection method is adapted to solve large, sparse, unstructured systems of linear equations. This row-projection technique is a direct method which can be interpreted as an oblique Kaczmarz-type algorithm, and is also related to other standard solution methods. When a sparsity-preserving pivoting strategy is incorporated, it is demonstrated that the technique can be superior, in terms of both fill-in and arithmetic complexity, to more standard sparse algorithms based on gaussian elimination. This is especially true for systems arising from stiff ordinary differential equations problems in chemical kinetics studies.