Lz. Lu et Cem. Pearce, ON THE MATRIX-SIGN-FUNCTION METHOD FOR SOLVING ALGEBRAIC RICCATI-EQUATIONS, Applied mathematics and computation, 86(2-3), 1997, pp. 157-170
This paper gives an improvement to the method of solving algebraic Ric
cati equations via use of the matrix sign function. We show that a 2n
x n or n x 2n system can be truncated to an n x n system and the solut
ion of the truncated system can be guaranteed to be Hermitian. We show
also, with standard numerical examples, that although the truncated e
quation has a larger condition number, its solution may actually make
the algebraic Riccati equation have smaller residual. In our numerical
experiment, using MATLAB, the solution of the truncated system needed
only about 26% of the number of floating-point operations that the or
iginal system did. (C) Elsevier Science Inc., 1997.