A Parallel Unsymmetric Inverse Iteration Solver.
Greg Henry · 1995
We describe a matrix multiply based block unsymmetric inverse iteration solver for upper Hessenberg matrices. Our kernel is robust in that it prevents overflow by scaling. It uses new techniques to ensure performance is not sacrificed when scaling is not necessary. Finally, we give results on a parallel implementation on an Intel Paragon TM supercomputer. Keywords: Parallel, Inverse Iteration, Unsymmetric Eigenvalue Problem, Intel Paragon TM supercomputer 1 Introduction Parallel unsymmetric inverse iteration often under-utilizes machine resources. This paper describes a robust kernel for the solution of Hessenberg systems of equations, and how it can be adapted for inverse iteration. Suppose H 2 ! n\\Thetan is a real upper Hessenberg matrix and B 2 ! n\\Thetam where b i is the i th column of B (1 i m). Let D be a diagonal matrix of size m. Typically, 1 m ! n: We wish to solve HX \\Gamma XD = BS (1) for X and S, where S is a diagonal matrix of scaling factors. The scali...