Numerical Analysis of Matrix Functions

| Description of the Project| Reports and Papers| Software| People| Conferences| Links| Contact us|

Description of the Project

This 3 year EPSRC funded project is concerned with functions f(A) of square matrices A. The importance of matrix functions lies in the diverse roles they play in the solution of problems in science and engineering. For example, certain differential equations can be solved explicitly in terms of matrix functions:

dy/dt = Ay implies y(t) = eAt .

The corresponding inverse problems, arising in system identification, can be solved by computing the matrix logarithm.

The aim of this project is to further our understanding of the theory, computation and application of matrix functions. New and improved algorithmic techniques will be developed for the computation of both general and particular functions, and made available in software. We also plan to investigate the problems affecting lattice quantum chromodynamics (QCD) computations with the aim of developing improved theory and methods. In developing theory and algorithms it is natural to treat general f as well as those particular f for which special techniques can be applied. Some of the research proposed applies to dense matrices and some to sparse matrices. However, we emphasize that most sparse f(A) techniques require the computation of f(B) for a dense (and much smaller) B. Therefore work for the dense case has immediate payoffs for the sparse case, too.


Reports and Papers

A bibliography of publications concerning the theory and computation of matrix functions.

Software

Matlab M-files for the Schur-Parlett algorithm for computing matrix functions are available in the tar file Funm_files.tar. The toolbox is distributed under this MIT license. This tar file contains a MEX-file swap.c that allows the algorithm to use the LAPACK routine xTREXC.

People

Grantholder

    Prof. Nick Higham is the Richardson Professor of Applied Mathematics at the University of Manchester.

Research Staff

    Dr. Philip Davies is a Research Associate in the Department of Mathematics at the University of Manchester.

Collaborators


Conferences


Links

    HEP-LAT(High Energy Physics LATtice gauge theory) preprint archive server.
    PCMF: Parallel Computation of Matrix Functions.
    Stanford Linear Accelerator Center (SLAC), Stanford Public Information REtrieval System (SPIRES). U.K. mirror
    The Worldwide Web Virtual Library: High-Energy Physics