The generalized Newton iteration for the matrix sign function

In this paper we present modified algorithms for computing deflating subspaces of matrix pairs using the matrix sign function. Our new algorithms achieve a considerable reduction of the computational cost of the generalized Newton iteration for the matrix sign function and improve the accuracy of the computed deflating subspaces. The matrix sign function is thus revealed as an effective technique for applications in which bases for the deflating subspaces are required. When partial or complete information about the eigenspectrum is desired, the matrix sign function can be used as an initial divide-and-conquer technique. The basic kernels involved in this iteration are especially appropriate for current high-performance architectures.