This paper presents a short survey of recent work on parallel implementations of Numerical Linear Algebra algorithms with emphasis on those relating to the solution of the symmetric eigenvalue problem on loosely coupled multiprocessor architectures. The vital operations in the formulation of most eigenvalue algorithms are matrix vector multiplication, matrix transposition, and linear system solution. Their implementations on several representative multiprocessor systems will be described, as well as parallel implementations of the following classes of eigenvalue methods : QR, bisection, divide-and-conquer, and Lanczos algorithm.

The Impact of Parallel Architectures on The Solution of Eigenvalue Problems

This is a bibliography on numerical methods. It also includes a number of other references on machine architecture, programming language, and other topics of interest to scientific computing. Certain conference proceedings and anthologies which have been published in book form are also listed.

A bibliography on parallel and vector numerical algorithms

: We propose a few implementations of the Alternating Direction Method for solving parabolic partial differential equations on multiprocessors. A careful complexity analysis of these implementations shows that, contrary to what is generally believed, the method can be made highly efficient on parallel architectures by using pipelining and variations of the classical Gaussian elimination algorithm for solving tridiagonal systems.

Alternating Direction Methods on Multiprocessors: An Extended Abstract.

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Alternating Direction Methods on Multiprocessors: An Extended Abstract.