A study of the Invariant Subspace Decomposition Algorithm for banded symmetric matrices
Christian H Bischof, X. Sun, Anna Tsao, T. Turnbull · University of North Texas Digital Library (University of North Texas) · 1994
In this paper, we give an overview of the Invariant Subspace Decomposition Algorithm for banded symmetric matrices and describe a sequential implementation of this algorithm. Our implementation uses a specialized routine for performing banded matrix multiplication together with successive band reduction, yielding a sequential algorithm that is competitive for large problems with the LAPACK QR code in computing all of the eigenvalues and eigenvectors of a dense symmetric matrix. Performance results are given on a variety of machines. 1 Introduction Computation of eigenvalues and eigenvectors is an essential kernel in many applications, and several promising parallel algorithms have been investigated [8, 11, 7]. The work presented in this paper is part of the PRISM (Parallel Research on Invariant Subspace Methods) Project, which involves researchers from Argonne National Laboratory, the Supercomputing Research Center, the University of California at Berkeley, and the University of Kent...