Vector and Parallel Processing – VECPAR’98

We survey some unusual eigenvalue problems arising in different applications. We show that all these problems can be cast as problems of estimating quadratic forms. Numerical algorithms based on the well-known Gauss-type quadrature rules and Lanczos process are reviewed for computing these quadratic forms. These algorithms reference the matrix in question only through a matrix-vector product operation. Hence it is well suited for large sparse problems. Some selected numerical examples are presented to illustrate the efficiency of such an approach.