A Modified Block Newton Iteration Forapproximating an Invariant Subspace of Asymmetric Matrixralf L

In this paper we propose a Modiied Block Newton Method for approximating an invariant subspace S and the corresponding eigenvalues of a symmetric matrix A. The method generates a sequence of matrices Z (k) which span subspaces S k approximating S. The matrices Z (k) are calculated via a Newton step applied to a special formulation of the block eigenvalue problem for the matrix A, followed by a Rayleigh-Ritz step which also yields the corresponding eigenvalue approximations. We show that for suuciently good initial approximations the subspaces S k converge to S in the sense that sin ' k with ' k := ](S k ; S) converges to zero Q-quadratically provided that the eigenvalues belonging to S are separated from the remaining ones.