Multicriteria optimization for nonunitary joint block diagonalization

Abstract

This paper deals with the nonunitary joint block diagonalization (JBD) of a set of given matrices for nonsquare mixing. As is known that the elimination of the degenerate solutions is a crucial problem in nonunitary JBD. Unlike the existing method, which optimizes a penalty term based least squares criterion to eliminate the degenerate solutions. In this paper we seek a well conditioned solution to nonunitary JBD instead. From this point of view, the nonunitary JBD problem is reformulated as a multicriteria optimization model. The resulting algorithm is numerically robust, and can be used in nonsquare mixing scenario. Moreover, it outperforms the existing JBD algorithms in terms of convergence rate and stability, which has been verified by our simulation results.