Eigenvalue Bounds for Saddle-Point Systems with Singular Leading Blocks

TL;DR

This paper establishes eigenvalue bounds for saddle-point matrices with singular blocks using augmentation, relating bounds to principal angles, and confirms findings through numerical experiments.

Contribution

It introduces a novel approach to bound eigenvalues of saddle-point systems with singular blocks based on principal angles and augmentation techniques.

Findings

Eigenvalue bounds depend on principal angles between matrix ranges and kernels.

Numerical experiments confirm the theoretical bounds.

The method applies to saddle-point matrices with singular leading blocks.

Abstract

We derive bounds on the eigenvalues of saddle-point matrices with singular leading blocks. The technique of proof is based on augmentation. Our bounds depend on the principal angles between the ranges or kernels of the matrix blocks. Numerical experiments validate our analytical findings.