Philip Knight

I've added a couple of papers that I've finished recently. I am currently very excited about matrix balancing. The problem is straighhtforward to state: find diagonal matrices D and E so that the norms of all the rows and columns of DAE are the same. I've found lots of interesting applications (e.g., preconditioning, data mining) and now I'm looking to compute it faster. I'm still interested in odd applications of Markov chains and I'm trying to learn more about inverse eigenvalue problems. If you've got anything interesting to tell me about these topics, let me know! I'd be more than happy to share my thoughts with you.

Some Publications

• The Sinkhorn-Knopp algorithm: theory and applications.
• The Hertz contact problem, coupled Volterra integral equations and a linear complementarity problem. With Alain Gauthier and Sean McKee.
• Weak lumpability in the k-SAT problem. With Michael Grinfeld.
• Spectral gap and cut-off in Markov chains. With Michael Grinfeld and Adri Olde-Daalhuis.
• Nonnormality and finite precision arithmetic in power method dynamics. With Michael Grinfeld and Harbir Lamba.
• Stability of finite-dimensional systems with indefinite damping. With Pedro Freitas and Michael Grinfeld.

Here's a picture that I've had up for a while. I think it's pretty. It illustrates the action of the power method on a 3x3 nonnormal matrix.

Last updated 18th May, 2006.