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On the inversion of polynomials of discrete Laplace matrices

Journal Article (2026)
Author(s)

S. S. Asghar (Universiteit Hasselt)

Q. Peng (Lancaster University, Universiteit Leiden)

F.J. Vermolen (Universiteit Hasselt, University of Johannesburg, TU Delft - Electrical Engineering, Mathematics and Computer Science)

Cornelis Vuik (TU Delft - Electrical Engineering, Mathematics and Computer Science)

Research Group
Numerical Analysis
DOI related publication
https://doi.org/10.1016/j.rinam.2026.100686 Final published version
More Info
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Publication Year
2026
Language
English
Research Group
Numerical Analysis
Journal title
Results in Applied Mathematics
Volume number
29
Article number
100686
Downloads counter
42
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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 previously known expressions of the inverse discretized Laplacian in one spatial dimension (Vermolen et al., 2022). The formalism is further extended to obtain closed form expressions for time-dependent problems.