The Impact of Parallel Architectures on the Solution of Eigenvalue Problems.
Abstract
The most significant impact on research in Scientific Computation, and Numerical Linear Algebra in particular, seems to have been brought about by the advent of vector and parallel computation. 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. A simple model will be given to analyse the complexity of parallel algorithms on several representative multiprocessor systems: a linear processor array (or ring), a two-dimensional processor grid and the hypercube. The vital operations in the formulation of most eigenvalue algorithms are matrix vector multiplication, matrix transposition, and linear system solution. Their implementations on the above architectures will be described, as well as parallel implementations of the following classes of eigenvalue methods: QR, bisection, divide-and-conquer, and Lanczos algorithm.
Document Details
- Document Type
- Technical Report
- Publication Date
- Dec 01, 1985
- Accession Number
- ADA163187
Entities
People
- Ilse C. F. Ipsen
- Youcef Saad
Organizations
- Yale University