USING THE MATRIX SIGN FUNCTION TO COMPUTE INVARIANT SUBSPACES

The matrix sign function has several applications in system theory and matrix computations. However, the numerical behavior of the matrix si gn function, and its associated divide-and-conquer algorithm for compu ting invariant subspaces, are still not completely understood. In this paper, we present a new perturbation theory for the matrix sign funct ion, the conditioning of its computation, the numerical stability of t he divide-and-conquer algorithm, and iterative refinement schemes. Num erical examples are also presented. An extension of the matrix-sign-fu nction-based algorithm to compute left and right deflating subspaces f or a regular pair of matrices is also described.