PERTURBATION ANALYSIS FOR ANTITRIANGULAR SCHUR DECOMPOSITION.

Let Z be an n X n complex matrix. A decomposition Z = U̅MUH is called an antitriangular Schur decomposition of Z if U is an n x n unitary matrix and M is an n x n antitriangular matrix. The antitriangular Schur decomposition is a useful tool for solving palindromic eigenvalue problems. However, there is no perturbation result for an antitriangular Schur decomposition in the literature. The main contribution of this paper is to give a perturbation bound of such decomposition and show that the bound depends inversely on Due to image rights restrictions, multiple line equation(s) cannot be graphically displayed., where XL and XU are the strictly lower triangular and upper triangular parts of X, XN = XL + XU, and Aup(Y) denotes the strictly upper antitriangular part of Y. The quantity √2/f(M) can be used to characterize the condition number of the decomposition, i.e., when √2/f(M) is large (or small), the decomposition problem is ill-conditioned (or well-conditioned). Numerical examples are presented to illustrate the theoretical result. [ABSTRACT FROM AUTHOR]