On the Inversion of Polynomials of Discrete Laplace Matrices

2025/11/24 by Asghar, Sabia, Peng, Qiyao, Vermolen, Fred +1 · 1 citation
#FOS: Mathematics #Numerical Analysis (math.NA)

paper · doi:10.48550/arxiv.2511.19724

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 \citepVermolen₂022. Several examples are given.

Citations

• A practical method for numerical evaluation of solutions of partial differential equations of the heat-conduction type

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