Double-shift-invert Arnoldi method for computing the matrix exponential (Q1756729)
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scientific article; zbMATH DE number 6996768
| Language | Label | Description | Also known as |
|---|---|---|---|
| English | Double-shift-invert Arnoldi method for computing the matrix exponential |
scientific article; zbMATH DE number 6996768 |
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Double-shift-invert Arnoldi method for computing the matrix exponential (English)
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21 December 2018
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This paper develops a double shift Arnoldi process and error bounds for approximating the matrix exponential as needed to solve evolution DEs. Its aim is to deal with DEs in large sparse discretized form for $10^6$ by $10^6$ or larger matrices. Numerical tests compare this method to and its advantages over single shift Arnoldi regarding the respective accuracies, run times, and needed iterations. The interested reader might also want to consult the multi shift Arnoldi process of \textit{M. S. Pranić} et al. [Numer. Linear Algebra Appl. 23, No. 6, 1007--1022 (2016; Zbl 1424.65042)].
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double shift Arnoldi
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matrix exponential
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evolution differential equation
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0.7899296879768372
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0.7708232998847961
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0.7684502601623535
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0.7558794617652893
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