A Hybrid Factorization Algorithm for Sparse Matrix with Mixed Precision Arithmetic

TL;DR

This paper introduces a hybrid LDU-factorization algorithm for large sparse matrices that combines iterative solvers with mixed precision arithmetic to maintain accuracy and improve efficiency.

Contribution

It proposes a novel hybrid factorization method that integrates iterative solvers with mixed precision arithmetic for large sparse matrices.

Findings

Achieves accurate factorization using mixed precision techniques.

Efficiently decomposes matrices into moderate and hard parts.

Maintains classical accuracy with reduced computational cost.

Abstract

A new hybrid algorithm for LDU-factorization for large sparse matrix combining iterative solver, which can keep the same accuracy as the classical factorization, is proposed. The last Schur complement will be generated by iterative solver for multiple right-hand sides using block GCR method with the factorization in lower precision as a preconditioner, which achieves mixed precision arithmetic, and then the Schur complement will be factorized in higher precision. In this algorithm, essential procedure is decomposition of the matrix into a union of moderate and hard parts, which is realized by LDU-factorization in lower precision with symmetric pivoting and threshold postponing technique.