Squeezing the most out of eigenvalue solvers on high-performance computers

AbstractThis paper describes modifications to many of the standard algorithms used in computing eigenvalues and eigenvectors of matrices. These modifications can dramatically increase the performance of the underlying software on high-performance computers without resorting to assembler language, without significantly influencing the floating-point operation count, and without affecting the roundoff-error properties of the algorithms. The techniques are applied to a wide variety of algorithms and are beneficial in various architectural settings

My Time at Enfield

This article centres around my time at Enfield College of Technology. The college was part of the revolution in higher education fostered by members of both the Labour and Conservative parties, and which found expression in the Robbins Committee, set up by Harold Macmillan's government, whose report was published in 1963. A lightly edited version of this article, without photographs, appears as Chapter 5 in the book Enfield Voices: The Birth of the People's Universities, edited by Tom Bourner and Tony Crilly and published in 2018. I am grateful to Tom and Tony, who were both colleagues at Enfield, for the opportunity to tell something of my story. Although certainly not unique, I was unusual in that I was a student on the Mathematics for Business, B.Sc., degree at Enfield College of Technology, and became a lecturer on the same degree the term after graduating. This article tells something of the story of my student life and working life, before, during and after Enfield

Workshop on Batched, Reproducible, and Reduced Precision BLAS

This report summarises the main points raised on a recent workshop discussing various extensions to the BLAS standard, held at the University of Tennessee in May 2016. In particular the discussions focused on batched, reproducible, and reduced precision BLAS extensions. Various members of the linear algebra community and representatives from industry were present to generate and evaluate ideas in each of these areas

An introduction to the quality of computed solutions

This report is concerned with the quality of the computed numerical solutions of mathematical problems. We give an introduction to ideas that are important in understanding and measuring the quality of computed solutions. In particular we review the ideas of condition, stability and error analysis, and their realisation in numerical software. A number of illustrative examples are given

A Survey of Numerical Aspects of Plane Rotations

In recent years the use of plane rotations in orthogonal factorizations has been increasing in popularity. This is in part due to modifications which enable computations with plane rotations to be carried out more quickly and in part due to the use of plane rotations in updating matrix factorizations and in other sparse applications. A review of Jacobi, Givens and modified plane rotations and of products of plane rotations is given. The review includes discussion of the computational details required to avoid underflow and overflow when computing plane rotations, storage of plane rotations and the stability of plane rotations. Mention is also made of the possibility of using plane rotations for pivoting