Successive Projection Method for Well-Conditioned Matrix Approximation Problems

Mirai Tanaka

doi:10.1109/LSP.2014.2303153

2014-04-01

PRE

Mirai Tanaka *

Kazuhide Nakata

DOI：10.1109/LSP.2014.2303153

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摘要

En 中文

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.

Keyword:

Covariance matrices

estimation

iterative algorithms

least squares approximations

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期刊

IEEE Signal Processing Magazine

IF:

9.6

论文数:

1.1W

被引数:

1.7W

机构

Institute of Science Tokyo

学者数:

3.2W

论文数: 2.7W

被引数: 117

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