The Matrix Computation Toolbox
11 Sep 2002
11 Sep 2002)
A collection of M-files for carrying out various numerical linear algebra tasks.
function [S, N] = signm(A)
%SIGNM Matrix sign decomposition.
% [S, N] = SIGNM(A) is the matrix sign decomposition A = S*N,
% computed via the Schur decomposition.
% S is the matrix sign function, sign(A).
% N. J. Higham, The matrix sign decomposition and its relation to the
% polar decomposition, Linear Algebra and Appl., 212/213:3-20, 1994.
[Q, T] = schur(A,'complex');
S = Q * matsignt(T) * Q';
% Only problem with Schur method is possible nonzero imaginary part when
% A is real. Next line takes care of that.
if ~any(imag(A)), S = real(S); end
if nargout == 2
N = S*A;