A convexity-like structure for polar decomposition with an application to distributed computing

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Podrobná bibliografie
Vydáno v:	arXiv.org (Dec 18, 2024), p. n/a
Hlavní autor:	Alimisis, Foivos
Další autoři:	Vandereycken, Bart
Vydáno:	Cornell University Library, arXiv.org
Témata:	Eigenvalues Matrix algebra Linear algebra Matrices (mathematics) Convexity Distributed processing
On-line přístup:	Citation/Abstract Full text outside of ProQuest
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Popis
Abstrakt:	We make a full landscape analysis of the (generally non-convex) orthogonal Procrustes problem. This problem is equivalent with computing the polar factor of a square matrix. We reveal a convexity-like structure, which explains the already established tractability of the problem and show that gradient descent in the orthogonal group computes the polar factor of a square matrix with linear convergence rate if the matrix is invertible and with an algebraic one if the matrix is singular. These results are similar to the ones of Alimisis and Vandereycken (2024) for the symmetric eigenvalue problem. We present an instance of a distributed Procrustes problem, which is hard to deal by standard techniques from numerical linear algebra. Our theory though can provide a solution.
ISSN:	2331-8422
Zdroj:	Engineering Database