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diff mftoolbox/riccati_xaxb.m @ 0:8f23314345f4 draft

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Create local repository for matrix toolboxes. Step #0 done.
author Antonio Pino Robles <data.script93@gmail.com>
date Wed, 06 May 2015 14:56:53 +0200
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--- /dev/null	Thu Jan 01 00:00:00 1970 +0000
+++ b/mftoolbox/riccati_xaxb.m	Wed May 06 14:56:53 2015 +0200
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+function X = riccati_xaxb(A,B)
+%RICCATI_XAXB  Solve Riccati equation XAX = B in positive definite matrices.
+%   X = RICCATI_XAXB(A,B) is the Hermitian positive definite
+%   solution to XAX = B, where A and B are Hermitian positive
+%   definite matrices.
+
+R = chol(A);
+S = chol(B);
+
+U = polar_newton(S*R');
+X = R\(U'*S);
+X = (X + X')/2;
+
+% [U,H] = polar_newton(R*S'); % Variant derived in solution of Problem 6.21.
+% X = R\(U*S);