The Generalized Newton Iteration forthe Matrix Sign Function

In this paper we present modiied algorithms for computing deeating subspaces of matrix pencils by means of the matrix sign function. Speciically, our new algorithms reduce the number of iterations to half, cut the cost of each Newton iteration by more than 50%, and improve the accuracy of the computed deeating subspaces. The matrix sign function is thus revealed as an eeective technique for applications where a part of the spectrum has to be identiied or only the deeating subspaces are required. When the complete spectrum is desired, the matrix sign function can be used as an initial divide-and-conquer technique. The high performance of the basic kernels involved in this iteration are also specially appropriate for current parallel architectures.