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Aggressively truncated Taylor series method for accurate computation of exponentials of essentially nonnegative matrices
Umeå University, Faculty of Science and Technology, High Performance Computing Center North (HPC2N). Umeå University, Faculty of Science and Technology, Department of Computing Science.
2014 (English)In: SIAM Journal on Matrix Analysis and Applications, ISSN 0895-4798, E-ISSN 1095-7162, Vol. 35, no 2, 317-338 p.Article in journal (Refereed) Published
Abstract [en]

Small relative perturbations to the entries of an essentially nonnegative matrix introduce small relative errors to entries of its exponential. It is thus desirable to compute the exponential with high componentwise relative accuracy. Taylor series approximation coupled with scaling and squaring is used to compute the exponential of an essentially nonnegative matrix. An a priori componentwise relative error bound of truncation is established, from which one can choose the degree of Taylor series expansion and the scale factor so that the exponential is computed with desired componentwise relative accuracy. To reduce the computational cost, the degree of the Taylor series expansion is chosen small, while the scale factor is chosen sufficiently large to achieve the desired accuracy. The rounding errors in the squaring stage are not serious as squaring is forward stable for nonnegative matrices. We also establish a posteriori componentwise error bounds and derive a novel interval algorithm for the matrix exponential of an essentially nonnegative matrix. Rounding error analysis and numerical experiments demonstrate the efficiency and accuracy of the proposed methods.

Place, publisher, year, edition, pages
SIAM publications , 2014. Vol. 35, no 2, 317-338 p.
Keyword [en]
matrix exponential, Taylor series, essentially nonnegative matrix, high relative accuracy algorithms
National Category
Mathematics
Identifiers
URN: urn:nbn:se:umu:diva-91874DOI: 10.1137/120894294ISI: 000338830100001OAI: oai:DiVA.org:umu-91874DiVA: diva2:738477
Available from: 2014-08-18 Created: 2014-08-18 Last updated: 2017-12-05Bibliographically approved

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Shao, Meiyue
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High Performance Computing Center North (HPC2N)Department of Computing Science
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CiteExportLink to record
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Citation style
  • apa
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Language
  • de-DE
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  • en-US
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  • nn-NO
  • nn-NB
  • sv-SE
  • Other locale
More languages
Output format
  • html
  • text
  • asciidoc
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