Numerical Analysis of Matrix Functions

Description of the Project
Reports and Papers
Software
People
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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
y(t) = e^{At} .
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.
A
bibliography
of publications concerning the theory and computation of matrix functions.
Matlab Mfiles for the SchurParlett 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 MEXfile
swap.c that allows the algorithm to use
the LAPACK routine xTREXC.
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