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Evaluating Matrix Functions by Resummations on Graphs: the Method of Path-Sums

Abstract:

We introduce the method of path-sums which is a tool for exactly evaluating a function of a discrete matrix with possibly non-commuting entries, based on the closed-form resummation of infinite families of terms in the corresponding Taylor series. If the matrix is finite, our approach yields the exact result in a finite number of steps. We achieve this by combining a mapping between matrix powers and walks on a weighted directed graph with a universal graph-theoretic result on the structure o...

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Publication status:
Published

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Publisher copy:
10.1137/120862880
Journal:
SIAM. J. Matrix Anal. and Appl., 34(2), 445-469, 2013 More from this journal
Volume:
34
Issue:
2
Pages:
445-469
Publication date:
2011-12-07
DOI:
EISSN:
1095-7162
ISSN:
0895-4798
Language:
English
Keywords:
Pubs id:
pubs:329386
UUID:
uuid:66e06a6c-0d18-4aca-82f4-9129d61c0183
Local pid:
pubs:329386
Source identifiers:
329386
Deposit date:
2012-12-19

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