On the Inversion of Polynomials of Discrete Laplace Matrices
Numerical Analysis
2026-02-12 v2 Numerical Analysis
Abstract
The efficient inversion of matrix polynomials is a critical challenge in computational mathematics. We design a procedure to determine the inverse of matrices polynomial of multidimensional Laplace matrices. The method is based on eigenvector and eigenvalue expansions. The method is consistent with previous expressions of the inverse discretized Laplacian in one spatial dimension \citep{Vermolen_2022}. Several examples are given.
Keywords
Cite
@article{arxiv.2511.19724,
title = {On the Inversion of Polynomials of Discrete Laplace Matrices},
author = {Sabia Asghar and Qiyao Peng and Fred Vermolen and Cornelis Vuik},
journal= {arXiv preprint arXiv:2511.19724},
year = {2026}
}
Comments
22 pages, 5 figures