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A Jacobi-like method for solving algebraic Riccati equations on parallel computers. (English) Zbl 0891.93033

A Jacobi-like method for computing the Hamiltonian-Schur form of a Hamiltonian matrix is suggested. The method is analogous to the Jacobi-like method of Eberlein for the computation of the Schur form of a general matrix. When used for Hermitian Hamiltonian matrices, the method is equivalent to the Kogbetliantz algorithm. Numerical experiments suggest a fast convergence. The method is used to solve continuous time Riccati equations.

MSC:

93B40 Computational methods in systems theory (MSC2010)
93B60 Eigenvalue problems
65F15 Numerical computation of eigenvalues and eigenvectors of matrices
15A24 Matrix equations and identities
65Y05 Parallel numerical computation