Numerical Linear Algebra and Computer Architecture : An Evolving Interaction

The aim of this report is to highlight the evolving interaction between computer architecture on the one hand and the design and analysis of algorithms for numerical linear algebra on the other. This report can best be described as a collection of pointers to aspects of the development processes of numerical linear algebra, and to various existing surveys and software. The rich variety of activity in design, analysis, comparison and evaluation of algorithms, new and old, is examined in the context of rapid technological and architectural advance. The characteristics of algorithms for linear algebra are discussed without going into mathematical details: There are references to important surveys that provide such details. Reflections on the practices of numerical linear algebra will, it is hoped, point to possibilities for and limitations of automating the “mapping” of algorithms onto high performance computers. †The author greatly acknowledges the support of the Science and Engineering Research Council (SERC Grant GR/F/04292) for this work. †Copyright 1993. All rights reserved. Reproduction of all or part of this work is permitted for educational or research purposes on condition that (1) this copyright notice is included, (2) proper attribution to the author or authors is made and (3) no commercial gain is involved. Technical Reports issued by the Department of Computer Science, Manchester University, are available by anonymous ftp from m1.cs.man.ac.uk (130.88.13.4) in the directory /pub/TR. The files are stored as PostScript, in compressed form, with the report number as filename. Alternatively, reports are available by post from The Computer Library, Department of Computer Science, The University, Oxford Road, Manchester M13 9PL, U.K.