A Stabilized Matrix Sign Function Algorithm for Solving Algebraic Riccati Equations

Authors:
Judith D. Gardiner
Affiliations:
-
Venue:
SIAM Journal on Scientific Computing
Year:
1997

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Cited 1

Algorithm 800: Fortran 77 subroutines for computing the eigenvalues of Hamiltonian matrices. I: the square-reduced method

ACM Transactions on Mathematical Software (TOMS)

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Abstract

Because of its suitability for parallel computation, the matrix sign function is a popular algorithm for solving the algebraic Riccati equation (ARE). The algorithm can be numerically unstable, however, even when combined with iterative refinement. This paper presents an enhanced algorithm which is shown to be backward stable under most circumstances. The method uses a combination of iterative refinement, scaling, and shifting, together with carefully chosen stopping criteria. An error analysis supports the algorithm modifications. Computational examples demonstrate the effectiveness of these techniques.