Lloyd N. Trefethen
Ph.D. Stanford University, 1982

My field is numerical analysis or scientific computing: the study of algorithms for solving the problems of continuous applied math-ematics. Much of my work within this area concerns non-normal matrices and operators and their pseudospectra. Some recent and ongoing activities are as follows.

Recent Ph.D. Toby Driscoll and I developed new domain decomposition algorithms for numerical conformal mapping and for La-place eigenvalue problems on polygons such as the problem underlying the question, "Can one hear the shape of a drum?".

Recent Ph.D. Kim-Chuan Toh and I developed new algorithms and results concerning convergence of large-scale nonsymmetric matrix iterations such as Arnoldi and GMRES, as well as their idealized counterparts such as the "Chebyshev polynomial of a matrix".

Ph.D. student Jeff Baggett and I investigated the process of breakdown of streamwise streaks that makes fluid flows at high Reynolds numbers unstable in practice, even though all the eigenmodes decay exponentially.

Ph.D. student Yohan Kim and I are investigating transient effects in Markov chains, such as the celebrated "cut-off" phenomenon in shuffling a deck of cards.

Ph.D. student Vicki Howle and I are investigating questions of eigenvalues, pseudo-eigenvalues, and the physics of musical instruments.

Ph.D. student Divakar Viswanath and I are investigating fundamental results to answer the question: how much do the pseudospectra of a matrix tell you about its behavior as measured by norms of operators? We are also developing a general theory of stability of numerical algorithms in the presence of rounding errors.

Finally, with a group of Ph.D. students and with Anne Trefethen of the Cornell Theory Center, I have been involved with the development of MultiMATLAB, an MPI-based extension of MATLAB that enables MATLAB users to run jobs conveniently on multiple processors of an SP-2 or a network of workstations.

A graduate textbook coauthored with David Bau, "Numerical Linear Algebra", is to be published soon by SIAM.

University Activities

Professional Activities



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Last modified: 2 November 1996 by Denise Moore (denise@cs.cornell.edu).