EU Regional School - Higham Seminar

Location: C.A.R.L Building, 2nd Floor, Room HO8

Prof. Nicholas Higham, Ph.D. - Multiprecision Algorithms

School of Mathematics, University of Manchester,UK


Today's computing environments offer multiple precisions of floating-point arithmetic, ranging from quarter precision (8 bits) and half precision (16 bits) to double precision (64 bits) and even quadruple precision (128 bits, available only in software), as well as arbitrary precision arithmetic (again in software). Exploiting the available precisions is essential in order to reduce the time to solution, minimize energy consumption, and (when necessary) solve ill-conditioned problems accurately.
In this mini-course we will describe the precision landscape, explain how we can exploit dierent precisions in numerical linear algebra, and discuss how to analyze the accuracy and stability of multiprecision algorithms.
An outline of the content is:
  • IEEE standard arithmetic and availability in hardware and software. Motivation for low precision from applications, including machine learning. Applications requiring high precision. Simulating low precision for testing purposes. Software for high precision. Challenges of implementing algorithms in low precision.
  • Basics of rounding error analysis. Examples of error analyses of algorithms, focusing on issues relating to low precision.
  • Solving linear systems using mixed precision: iterative renement, hybrid direct-iterative methods. Multiprecision algorithms for matrix functions, focusing on the matrix logarithm.