Optimized scaling and squaring for matrix functions appearing in exponential integrators

The study explores algorithms for evaluating matrix φ functions, focusing on the scaling and squaring method, which combines approximation formulas with double-angle relations. Despite its effectiveness, the method's optimal degree of the formula remains underexplored due to the computational b...

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Bibliographic Details
Published inJSIAM Letters Vol. 17; pp. 1 - 4
Main Author Nakamura, Shinsuke
Format Journal Article
LanguageEnglish
Published The Japan Society for Industrial and Applied Mathematics 2025
Subjects
matrix φ function
optimal degree
scaling and squaring
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ISSN1883-0609
1883-0617
DOI10.14495/jsiaml.17.1

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Summary:The study explores algorithms for evaluating matrix φ functions, focusing on the scaling and squaring method, which combines approximation formulas with double-angle relations. Despite its effectiveness, the method's optimal degree of the formula remains underexplored due to the computational burden of matrix multiplications within the relations. To address this, we propose an alternative method that achieves equivalence to these relations without the extensive use of matrix multiplications. Furthermore, we determine the optimum degree for the approximation formula.
ISSN:1883-0609
1883-0617
DOI:10.14495/jsiaml.17.1