A Sparse-Sparse Iteration for Computing a Sparse Incomplete Factorization of the Inverse of an SPD Matrix

TL;DR

This paper introduces a new sparse-sparse iterative method to compute a sparse approximate inverse of SPD matrices, serving as an effective preconditioner for conjugate gradient solutions.

Contribution

It proposes a novel sparse-sparse iteration technique for incomplete inverse factorization, improving preconditioning efficiency for SPD linear systems.

Findings

The method produces effective sparse approximate inverses.

Numerical experiments show competitive performance.

The approach enhances convergence in iterative solvers.

Abstract

In this paper, a method via sparse-sparse iteration for computing a sparse incomplete factorization of the inverse of a symmetric positive definite matrix is proposed. The resulting factorized sparse approximate inverse is used as a preconditioner for solving symmetric positive definite linear systems of equations by using the preconditioned conjugate gradient algorithm. Some numerical experiments on test matrices from the Harwell-Boeing collection for comparing the numerical performance of the presented method with one available well-known algorithm are also given.