The matrix sign function method and the computation of invariant subspaces. (English) Zbl 0874.65031

Byers, Ralph; He, Chunyang; Mehrmann, Volker

SIAM J. Matrix Anal. Appl. 18, No. 3, 615-632 (1997).

Summary: A perturbation analysis shows that if a numerically stable procedure is used to compute the matrix sign function, then it is competitive with conventional methods for computing invariant subspaces. Stability analysis of the Newton iteration improves an earlier result of R. Byers [Computational and combinatorial methods in systems theory, Sel. Pap. 7th Int. Symp. Math. Theory Networks Syst., Stockholm 1986, 185-200 (1986; Zbl 0597.65032)[and confirms that ill-conditioned iterates may cause numerical instability. Numerical examples demonstrate the theoretical results.

MSC:

65F30	Other matrix algorithms (MSC2010)
65F15	Numerical computation of eigenvalues and eigenvectors of matrices

Keywords:

matrix sign function; invariant subspaces; stability; Newton iteration; numerical examples

Citations:

Zbl 0597.65032

Software:

LAPACK