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Solvability of matrix-exponential equations

Abstract:

We consider a continuous analogue of (Babai et al. 1996)’s and (Cai et al. 2000)’s problem of solving multiplicative matrix equations. Given k + 1 square matrices A1,..., Ak, C, all of the same dimension, whose entries are real algebraic, we examine the problem of deciding whether there exist non-negative reals t1,..., tk such that k/Π/i=1 exp(Ai ti) = C. We show that this problem is undecidable in general, but decidable under the assumption that the matrices A1, ..., Ak commute. Our results ...

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Publication status:
Published
Peer review status:
Peer reviewed
Version:
Accepted manuscript

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Publisher copy:
10.1145/2933575.2934538

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Department:
St Johns College
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Department:
Oxford, MPLS, Computer Science
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Department:
St Cross College
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Department:
Green Templeton College
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Funding agency for:
Sousa Pinto, J
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Publisher:
ACM/IEEE Symposium on Logic in Computer Science Publisher's website
Publication date:
2016-08-05
Acceptance date:
2016-04-04
DOI:
Pubs id:
pubs:619304
URN:
uri:b24e9e23-7fd3-418f-83bb-5820fa57f5d5
UUID:
b24e9e23-7fd3-418f-83bb-5820fa57f5d5
Local pid:
pubs:619304

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