Alternating-projection algorithms for operator-theoretic calculations

We show how alternating-projection algorithms can be used to solve a variety of operator-theoretic problems, including deciding complete positivity, computing completely bounded norms, computing norms of Schur multipliers, and matrix completion/approximation problems.

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Bibliographic Details
Published in:Linear algebra and its applications 2006-12, Vol.419 (2), p.710-734
Main Author: Zarikian, Vrej
Format: Article
Language:English
Subjects:
Algebra
Alternating-projection algorithm
Completely bounded map
Completely positive map
Exact sciences and technology
Linear and multilinear algebra, matrix theory
Mathematics
Matrix completion
Schur multiplier
Sciences and techniques of general use
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Description
Summary:We show how alternating-projection algorithms can be used to solve a variety of operator-theoretic problems, including deciding complete positivity, computing completely bounded norms, computing norms of Schur multipliers, and matrix completion/approximation problems.
ISSN:0024-3795
1873-1856
DOI:10.1016/j.laa.2006.06.012