Quasiseparable LU decay bounds for inverses of banded matrices

TL;DR

This paper introduces new exponential decay bounds for the inverses of banded matrices using quasiseparable representations, which are computationally efficient and do not depend on spectral data, especially useful for nonsymmetric or indefinite matrices.

Contribution

The paper presents novel decay bounds for matrix inverses based on quasiseparable representations, avoiding spectral computations and applicable to a broader class of matrices.

Findings

Bounds are easily computable and rely on diagonal dominance.

Numerical experiments demonstrate advantages for nonsymmetric and indefinite matrices.

Bounds outperform existing methods in certain cases.

Abstract

We develop new, easily computable exponential decay bounds for inverses of banded matrices, based on the quasiseparable representation of Green matrices. The bounds rely on a diagonal dominance hypothesis and do not require explicit spectral information. Numerical experiments and comparisons show that these new bounds can be advantageous especially for nonsymmetric or symmetric indefinite matrices.