Lloyd N. Trefethen

Lloyd N. Trefethen
Professor
lnt@cs.cornell.edu
http://www.cs.cornell.edu/home/lnt/lnt.html
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

Director: Graduate Studies, Computer Science Department
Member: Applied Mathematics Program and Colloquium Committees; University Program Review Committee; Engineering College Teaching Awards Committee

Professional Activities

Editorial Boards: SIAM Review; SIAM Journal on Numerical Analysis; Journal of Computational and Applied Mathematics; Japan Journal of Industrial and Applied Mathematics; Numerische Mathematik
Member: SIAM Council; Fox Prize in Numerical Analysis Committee
Board of Directors: ACM SIGNUM (Special Interest Group on Numerical Mathematics)

Lectures

Non-normality, nonlinearity, and transition to turbulence. Joint invited lecture, Annual Conference of the Canadian Applied Mathematics Society and Canadian Symposium of Fluid Dynamics, Winnipeg, May 1996.
____. Applied Mathematics Colloquium, University of Strathclyde, Glasgow, March 1996.
____. Applied Mathematics Colloquium, University of Dundee, Dundee, March 1996.
____. Applied and Engineering Mathematics Seminar, University of Newcastle, March 1996.
____. Applied Mathematics Colloquium, Oxford University, March 1996.
____. Fluid Mechanics Colloquium, DAMTP, University of Cambridge, March 1996.
____. Fluid Mechanics Colloquium, DAMTP, University of Leeds, March 1996.
____. Joint Applied and Numerical Mathematics Colloquium, University of Manchester, March 1996.
____. Applied Mathematics Colloquium, Imperial College, London, March 1996.
____. Applied Mathematics Colloquium, University of Bath, March 1996.
The Chebyshev polynomial of a matrix. Approximation Day Conference, Department of Applied Mathematics and Theoretical Physics, University of Cambridge, March 1996.
When non-normality meets nonlinearity. Center for Nonlinear and Complex Systems Colloquium, Duke University, February 1996.
Computational mathematics in the 1990s. Undergraduate Mathematics Lecture, Duke University Undergraduate Math Union, February 1996.
Random triangular matrices. American Math. Soc., Kent, OH, November 1995.
When non-normality meets nonlinearity. Invited Lecture. Eigenvalues and Beyond Workshop, CERFACS, Toulouse, France, October 1995.
Random triangular matrices. IMA Conference on Linear Algebra and Its Applications, Manchester, UK, July 1995.
Why Gaussian elimination works even though it is unstable. Third ICIAM Congress on Industrial and Applied Mathematics, Hamburg, Germany, July 1995.

Publications

Calculation of pseudospectra by the Arnoldi iteration. SIAM Journal on Scientific Computing 17 (1996), 1-15 (with K. Toh).

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