The solution of large dense linear systems is a key application of parallel computers and an area where we have a body of well established high performance solutions. It is the area popularize by the Linpack benchmark, featured in the recent TFLOPS announcement. This lecture has two parts. The first part motivates the area by describing a class of computational electrodynamics problems that depend heavily upon the soltuion of dense linear systems. The second part describes the basic computational aspects of the problem. We start out with a review of Gaussian elimination and LU factorization. Then we discuss pivoting for stability. The last topic for this lecture will be to restructuring the computation and increase data-reuse. We will discuss the BLAS (basic linear algebra subroutines) Follow-on lectures will delve into high performance solutions.
"Electromagnetic Scattering Calculations on the Intel Touchstone Delta" by Cwik, Patterson, and Scott, Proceedings of IEEE Supercomputing '92, pp. 538 -542.
Jim Demmel's Lecture Notes: Lecture 14, 2/29/96: Design and Implementation of LAPACK and ScaLAPACK.
Numerical Linear Algebra chapter of the Computational Science Education Project.
Numerical Linear Algebra: Math 221 home page and many links from there.