Product of two positive contractions
Chi-Kwong Li, Diane Christine Pelejo, Kuo-Zhong Wang
TL;DR
This paper characterizes matrices that are products of two positive semidefinite projections, providing theoretical conditions and a MATLAB implementation to verify and construct such matrices.
Contribution
It offers new characterizations for matrices as products of two positive projections and develops a MATLAB tool for verification and construction.
Findings
Characterizations of matrices as products of two positive projections
A MATLAB program to check the conditions and construct the projections
Application of alternating projections theory to this problem
Abstract
Several characterizations are given for a square matrix that can be written as the product of two positive (semidefinite) projections. Based on one of these characterizations, and the theory of alternating projections, a Matlab program is written to check the condition and construct the two positive projections whose product equal to the given matrix, if they exist.
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Taxonomy
TopicsMatrix Theory and Algorithms · Advanced Optimization Algorithms Research · Numerical methods for differential equations