On the matrix-sign-function method for solving algebraic Riccati equations

摘要

This paper gives an improvement to the method of solving algebraic Riccati equations via use of the matrix sign function. We show that a 2n × n or n × 2n system can be truncated to an n × n system and the solution of the truncated system can be guaranteed to be Hermitian. We show also, with standard numerical examples, that although the truncated equation 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 original system did.