The investigation of Jacobi-type methods for the solution of the algebraic eigenproblem on parallel architectures is proposed here. Both symmetric and non-symmetric problems are considered, as is the generalized problem. Interest in this general area of numerical linear algebra has increased markedly since parallel machines appeared on the market; these machines already play an important role in scientific computing, and parallel algorithms present an important challenge. Jacobi-type algorithms are ideally suited for a parallel multiprocessor environment; recently they have been found competitive with standard serial methods on both shared memory multiprocessors and serial vector machines for the singular value problem. New approaches are shown which lead to an extension to the eigenvalue problem for both symmetric and non-symmetric matrices. One-sided Jacobi methods are introduced here, and compared with block Jacobi implementations. These methods may be regarded as a factored form of a sequence of similarity transformations which may be extended to non- unitary transformations. Probably the most important goal of the project is the experimental comparison of Jacobi methods with other methods which have become standard for serial computation on both the symmetric and non-symmetric eigenvalue/vector problems.^R JUSTIFICATION
