Contact Details
| Room No. | L932 |
|---|---|
| Telephone | +44 (0)141 548 3818 |
| Fax | +44 (0)141 548 3345 |
| p.a.knight@strath.ac.uk |
Research Interests
Matrix Computations
- Link analysis of web-like graphs
- Perturbation of graphs
- Algorithms for matrix balancing
- Preconditioning
Selected Publications
SIMAX, 2008, 30(1), 261-275.
J. Comput. Appl. Math., 2007, 206, 322-340.
Appl. Math. Lett., 2000, 13, 49-53.
Vacancies & Studentships
Matrix Balancing: Algorithms and Applications
Reference No.: PK1
Supervisor: Dr Philip Knight
Date Advertised: 6th February 2007
Please contact Dr Philip Knight for further information.
For at least 70 years, scientists in a wide variety of disciplines have attempted to transform square nonnegative matrices into doubly stochastic form by applying diagonal scalings.
That is, given a square nonnegative matrix A, find diagonal matrices D and E so that P = DAE is doubly stochastic.
Motivation for achieving the balance include interpreting economic data, preconditioning sparse matrices, understanding traffic circulation and ordering nodes in a graph.
The aim of this project is to develop fast methods to solve this problem, and to apply these methods to practical problems.
One approach for finding fast methods is to rephrase the balancing problem as a nonlinear equation and to look to adapt standard numerical methods for solving nonlinear equations.
This can be done successfully, but robustness of the resulting methods is a concern.
Another approach is to treat the problem as an eigenvalue problem with noisy data. This formulation offers some exciting challenges.
As well as looking to improve existing methods in the application areas outlined above, the balancing can be used to solve optimisation problems.
If theoretical results can be matched in practice, there is great potential in this area, too.