Successive Projection Method for Well-Conditioned Matrix Approximation Problems

Matrices are often required to be well-conditioned in a wide variety of areas including signal processing. Problems to find the nearest positive definite matrix or the nearest correlation matrix that simultaneously satisfy the condition number constraint and sign constraints are presented in this pa...

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Bibliographic Details
Published in:IEEE signal processing letters 2014-04, Vol.21 (4), p.418-422
Main Authors: Tanaka, Mirai, Nakata, Kazuhide
Format: Article
Language:English
Subjects:
Algorithms
Approximation
Approximation algorithms
Correlation
Covariance matrices
estimation
Intersections
iterative algorithms
Least squares approximations
Mathematical analysis
Polyhedrons
Projection
Signal processing
Signal processing algorithms
Symmetric matrices
Tin
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Summary:Matrices are often required to be well-conditioned in a wide variety of areas including signal processing. Problems to find the nearest positive definite matrix or the nearest correlation matrix that simultaneously satisfy the condition number constraint and sign constraints are presented in this paper. Both problems can be regarded as those to find a projection to the intersection of the closed convex cone corresponding to the condition number constraint and the convex polyhedron corresponding to the other constraints. Thus, we can apply a successive projection method, which is a classical algorithm for finding the projection to the intersection of multiple convex sets, to these problems. The numerical results demonstrated that the algorithm effectively solved the problems.
ISSN:1070-9908
1558-2361
DOI:10.1109/LSP.2014.2303153