Stable and Reliable Computation of Eigenvectors of Large Profile Matrices

Independent eigenvector computation for a given set of eigenvalues of typical engineering eigenvalue problems still is a big challenge for established subspace solution methods. The inverse vector iteration as the standard solution method often is not capable of reliably computing the eigenvectors of a cluster of bad separated eigenvalues. The following contribution presents a stable and reliable solution method for independent and selective eigenvector computation of large symmetric profile matrices. The method is an extension of the well-known and well-understood QR-method for full matrices thus having all its good numerical properties. The effects of finite arithmetic precision of computer representations of eigenvalue/eigenvector solution methods are analysed and it is shown that the numerical behavior of the new method is superior to subspace solution methods