y(t) = eAt .
y(t) = eAt .
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
Schur Algorithm for Computing Matrix pth Roots
by Matthew Smith.
SIAM J. Matrix Anal. Appl. 24(4): 971-989.
A
Schur-Parlett Algorithm for Computing Matrix Functions
by Philip Davies and
Nick Higham.
SIAM J. Matrix Anal. Appl., 25(2):464-485, 2003.
Updating the Singular Value Decomposition
by Philip Davies and
Matthew Smith.
NA Report 405, August 2002.
In
J. Comput. Appl. Math., 170:145-167, 2004.
Computing the Matrix Cosine
by Nick Higham and
Matthew I. Smith.
Numerical Algorithms, 34:13-26, 2003.
Computing f(A)b for Matrix Functions f
by Philip Davies and
Nick Higham.
NA Report 436, November 2003.
Computing the Polar Decomposition and the Matrix Sign Decomposition
in Matrix Groups
(With D. Steven Mackey,
Niloufer Mackey and
Françoise Tisseur),
SIAM J. Matrix Anal. Appl., 25(4):1178-1192, 2004.
Structured Conditioning of Matrix Functions
by Philip Davies.
The Electronic Journal of Linear Algebra, 11:132-161, 2004.
Final Report on the project, April 2004.
Prof. Nick Higham
is the Richardson Professor of Applied Mathematics
at the University of Manchester.
Dr. Philip Davies
is a Research Associate in the Department of Mathematics at the
University of Manchester.
Matthew Smith
is a Research Student in the Department of Mathematics at the
University of Manchester. Matthew graduated in December 2002.
His thesis,
Numerical Computation of Matrix Functions is available for download.
19th Biennial Dundee Conference on Numerical Analysis,
June 2001.
SIAM Annual Meeting, San Diego, July 2001.
Householder Symposium XV,
Peebles, Scotland, June 2002.
Spectral Theory Network Conference IV, University of Edinburgh,
June 23-25, 2003.
20th Biennial Dundee Conference on Numerical Analysis,
June 24-27, 2003.
Spectral Theory Network Conference IV, University of Edinburgh, June
2003.
Third International Workshop on Numerical Analysis and Lattice QCD,
Edinburgh, 30 June - 4 July, 2003.
28th Conference of the Dutch-Flemish Numerical Analysis Communities,
Woudschoten Conference Centre, Zeist, The Netherlands,
October 2003.
Workshop on Theory and Numerics of Matrix Eigenvalue Problems,
Banff International Research Station, November 2003
New Frontiers in Computational Mathematics Workshop,
University of Manchester, January 10-11, 2004.
HEP-LAT(High Energy
Physics LATtice gauge theory)
preprint archive server.
LAPACK Users' Guide , Third edition.
LAPACK software.
LAPACK Working Notes.
Matrix Market
PCMF: Parallel Computation of
Matrix Functions.
QCD Matrices
Stanford Linear
Accelerator Center (SLAC),
Stanford Public
Information REtrieval
System (SPIRES).
U.K. mirror
UKQCD
Collaboration
The Worldwide Web Virtual
Library: High-Energy Physics