Eigenvalue Bounds for Symmetric, Multiple Saddle-Point Matrices with SPD Preconditioners
Abstract
We derive the eigenvalue bounds for symmetric block-tridiagonal multiple saddle-point systems preconditioned with the symmetric positive definite (SPD) preconditioner proposed by J. Pearson and A. Potschka in 2024 and further studied by L. Bergamaschi and coauthors, and for double saddle-point problems with inexact Schur complement matrices. The analysis applies to an arbitrary number of blocks. We validate the proposed estimates with both synthetic and realistic test problems, and show the good performance of the proposed preconditioner under the condition that the Schur complements are accurately approximated.
Fields of Study & Subjects
Matrix Theory and Algorithms
Electromagnetic Scattering and Analysis
Tensor decomposition and applications
Publication details
- Journal / source
- Algorithms
- Publisher
- MDPI AG
- Volume
- 19
- Issue
- 5
- Pages
- 359–359
- Publication date
- 4 May 2026
- Language
- EN