TRUNCATED QZ METHODS FOR LARGE SCALE GENERALIZED EIGENVALUE PROBLEMS
D. C. Sorensen · Rice Research Repository (Rice University) · 1998
. This paper presents three methods for the large scale generalized eigenvalue problem Ax = Bx: These methods are developed within a subspace projection framework as a truncation and modification of the QZ-algorithm for dense problems that is suitable for computing partial generalized Schur decompositions of the pair (A; B). A generalized partial reduction to condensed form is developed by analogy with the Arnoldi process. Then truncated forward and backward QZ iterations are introduced to derive generalizations of the Implicitly Restarted Arnoldi Method and the Truncated RQ method for the large scale generalized problem. These two methods require accurate solutions of linear systems at each step of the iteration. Relaxing these accuracy requirements forces us to introduce non-Krylov projection spaces that lead most naturally to block variants of the QZ iterations. A two-block method is developed that incorporates k approximate Newton corrections at each iteration. An important feat...