Approximation of functions of large matrices with Kronecker structure

2015/03/09 by Michele Benzi, Valeria Simoncini, Benzi, Michele +1 · 3 citations
Computer Science · Mathematics · #FOS: Mathematics #Matrix Theory and Algorithms #Numerical Analysis (math.NA) #Numerical methods for differential equations #Tensor decomposition and applications

paper · pdf · doi:10.48550/arxiv.1503.02615

openalex publication_date 2015/03/09 · openalex created_date 2025/10/10 · openalex updated_date 2026/08/01

Abstract

We consider the numerical approximation of f(\cal A)b where b∈\mathbb R^N and \cal A is the sum of Kronecker products, that is \cal A=M₂ ⊗ I + I ⊗ M₁∈\mathbb R^{N× N}. Here f is a regular function such that f(\cal A) is well defined. We derive a computational strategy that significantly lowers the memory requirements and computational efforts of the standard approximations, with special emphasis on the exponential function, for which the new procedure becomes particularly advantageous. Our findings are illustrated by numerical experiments with typical functions used in applications.

Citations

• CONTEST
• Nineteen Dubious Ways to Compute the Exponential of a Matrix, Twenty-Five Years Later

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