Article ID Journal Published Year Pages File Type
4598987 Linear Algebra and its Applications 2015 20 Pages PDF
Abstract

Non-Orthogonal Joint Diagonalization (NOJD) of a given real symmetric matrix set A={Aj}j=0p is to find a nonsingular matrix W   such that W⊤AjWW⊤AjW for j=0,1,…,pj=0,1,…,p are all as diagonal as possible. If the columns of the solution W are all required to be unit length, we call such NOJD problem as the Normalized NOJD (NNOJD) problem. In this paper, we discuss the perturbation theory for NNOJD as an optimization problem. Based on the perturbation analysis of general constrained optimization problem given in [16], we obtain an upper bound for the distance between an approximated solution of the perturbed optimal problem and the set of exact joint diagonalizers. As corollaries, a perturbation bound and an error bound are also given. Numerical examples validate the bounds.

Related Topics
Physical Sciences and Engineering Mathematics Algebra and Number Theory
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