A novel nonsymmetric K_-Lanczos algorithm for the generalized nonsymmetric K_-eigenvalue problems

Abstract

In this article, we present a novel algorithm, named nonsymmetric K---Lanczos algorithm, for computing a few extreme eigenvalues of the generalized eigenvalue problem Mx = lambda Lx, where the matrices M and L have the so-called K-+/--structures. We demonstrate a K---tridiagonalization procedure preserves the K-+/--structures. An error bound for the extreme K---Ritz value obtained from this new algorithm is presented. When compared with the class nonsymmetric Lanczos approach, this method has the same order of computational complexity and can be viewed as a special 2 x 2-block nonsymmetric Lanczos algorithm. Numerical experiments with randomly generated K---matrices show that our algorithm converges faster and more accurate than the nonsymmetric Lanczos algorithm. (C) Elsevier Science Inc., 1997