Work

Eigenvalue bounds for preconditioned symmetric multiple saddle-point matrices with block-triangular preconditioners

Year: 2026

Type: preprint

Abstract: We develop eigenvalue bounds for symmetric, block-tridiagonal multiple saddle-point linear systems, preconditioned with block-triangular matrices, based on approximate Schur complements. Irrespective on the number of blocks, we prove that all complex eigenvalues, with nontrivial imaginary part, are strictly contained in a circle within the complex plane, with center 1. The real and positive eigenvalues are bounded in terms of the extremal roots of a sequences of parametric polynomials. Numerical results reveal that the bounds describe very well the eigenvalue distribution of the preconditioned matrix.

Source: arXiv (Cornell University)

DOI: 10.48550/arxiv.2608.24203

Authors: Bergamaschi, Luca, Bergamaschi, Michele, Pearson, John W.

Institutions: University of Padua, University of Edinburgh

Topic: Matrix Theory and Algorithms

Subfield: Computational Theory and Mathematics

Field: Computer Science

Domain: Physical Sciences

Open Access status: green

Funders: Istituto Nazionale di Alta Matematica "Francesco Severi", Università degli Studi di Padova, Gruppo Nazionale per il Calcolo Scientifico, Engineering and Physical Sciences Research Council

Award: Randomized Numerical Linear Algebra for Optimization and Control of PDEs

OpenAlex ID: W7204254677

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