Lanczos Algorithms for Large Symmetric Eigenvalue Computations

First published in 1985, this book presents background material, descriptions, and supporting theory relating to practical numerical algorithms for the solution of huge eigenvalue problems. This book deals with 'symmetric' problems. However, in this book, 'symmetric' also encompasses numerical procedures for computing singular values and vectors of real rectangular matrices and numerical procedures for computing eigenelements of nondefective complex symmetric matrices. Although preserving orthogonality has been the golden rule in linear algebra, most of the algorithms in this book conform to that rule only locally, resulting in markedly reduced memory requirements. Additionally, most of the algorithms discussed separate the eigenvalue (singular value) computations from the corresponding eigenvector (singular vector) computations. This separation prevents losses in accuracy that can occur in methods which, in order to be able to compute further into the spectrum, use successive implicit deflation by computed eigenvector or singular vector approximations.

Dr. Jane K. Cullum is a member of the Technical Staff of the Computer and Computational Sciences Division at Los Alamos National Laboratory Dr. Ralph A. Willoughby (1923-2001) was a member of the Research Staff in the Mathematical Sciences Department in IBM Research from 1957-1991. He organized the first Symposium on Sparse Matrices (1968), and some have called him the "father" of sparse matrix theory. In addition to his work with Dr. Cullum on eigenvalue algorithms, he is also well known for his important contributions (with his colleagues at IBM) to the symbolic factorization of sparse matrices and to methods for the solution of stiff systems of differential equations