Multiprocessor Jacobi algorithms for dense symmetric eigenvalue and singular value decompositions

Two parallel algorithms are presented based on Jacobi's method for real symmetric matrices to determine the complete eigensystem of a dense real symmetric matrix and the singular value decomposition of rectangular matrices on a multiprocessor. The intent is to study the advantages of using Jacobi and Jacobi-like schemes over new and existing EISPACK and LINPACK routines on an Alliant FX/8 computer system. For the dense symmetric eigenvalue problem, promising results are shown for small-order matrices. A ''one-sided'' Jacobi-like algorithm which produces the singular value decomposition of a rectangular matrix is shown to provide superior performance for rectangular matrices in which the number of rows is much larger than the number of columns. 17 refs., 9 figs., 5 tabs.