Van Loan, Charles F.
(2006)
*A Study of the Matrix Exponential.*
[MIMS Preprint]

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## Abstract

This report brings together a wide variety of facts concerning the matrix exponential. Against a background of familiar results, we present an analysis of matrix functions (the exponential in particular) which exploits the Schur decomposition theorem. This helps us explore the behavior of a function of a matrix whose eigensystem is poorly conditioned. Finally, we investigate Pade approximation of the matrix exponential and feature in the discussion a potentially useful inverse error analysis.

Item Type: | MIMS Preprint |
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Additional Information: | This EPrint is a reissue of the 1975 technical report of the same title. It should be cited as "Charles F. Van Loan. A study of the matrix exponential. Numerical Analysis Report No. 10, University of Manchester, Manchester, UK, August 1975. Reissued as MIMS EPrint 2006.397, Manchester Institute for Mathematical Sciences, The University of Manchester, UK, November 2006". |

Uncontrolled Keywords: | matrix function, matrix exponential, Pade approximation, matrix polynomial evaluation, scaling and squaring method, MATLAB, expm, backward error analysis, |

Subjects: | MSC 2010, the AMS's Mathematics Subject Classification > 15 Linear and multilinear algebra; matrix theory MSC 2010, the AMS's Mathematics Subject Classification > 65 Numerical analysis |

Depositing User: | Nick Higham |

Date Deposited: | 06 Nov 2006 |

Last Modified: | 08 Nov 2017 18:18 |

URI: | http://eprints.maths.manchester.ac.uk/id/eprint/644 |

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