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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);