Title :
A note on the complex matrix procrustes problem
Author :
Kiskiras, J. ; Halikias, G.D.
Author_Institution :
Control Engineering Research Centre, School of Engineering and Mathematical Sciences, City University, Northampton Square, London EC1V 0HB, U.K.
Abstract :
This note outlines an algorithm for solving the complex “matrix Procrustes problem”. This is a least-squares approximation over the cone of positive semi-definite Hermitian matrices, which has a number of applications in the areas of Optimization, Signal Processing and Control. The work generalises the method of [1], who obtained a numerical solution to the real-valued version of the problem. It is shown that, subject to an appropriate rank assumption, the complex problem can be formulated in a real setting using a matrix dilation technique, for which the method of [1] is applicable. However, this transformation results in an over-parametrisation of the problem and, therefore, convergence to the optimal solution is slow. Here an alternative algorithm is developed for solving the complex problem, which exploits fully the special structure of the dilated matrix. The advantages of the modified algorithm are demonstrated via a numerical example.
Keywords :
Approximation algorithms; Eigenvalues and eigenfunctions; Least squares approximations; Optimization; Symmetric matrices; Tin; Cone of positive semidefinite matrices; Least-squares approximation; Matrix Procrustes problem;
Conference_Titel :
European Control Conference (ECC), 2003
Conference_Location :
Cambridge, UK
Print_ISBN :
978-3-9524173-7-9