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
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
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.
- Director: Graduate Studies, Computer Science Department
- Member: Applied Mathematics Program and Colloquium Committees;
University Program Review Committee; Engineering College Teaching
- 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
- 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
- ____. Fluid Mechanics Colloquium, DAMTP, University of Cambridge,
- ____. Fluid Mechanics Colloquium, DAMTP, University of Leeds,
- ____. Joint Applied and Numerical Mathematics Colloquium,
University of Manchester, March 1996.
- ____. Applied Mathematics Colloquium, Imperial College, London,
- ____. Applied Mathematics Colloquium, University of Bath, March
- 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,
- When non-normality meets nonlinearity. Invited Lecture.
Eigenvalues and Beyond Workshop, CERFACS, Toulouse, France, October
- 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.
- Calculation of pseudospectra by the Arnoldi iteration. SIAM
Journal on Scientific Computing 17 (1996), 1-15 (with K. Toh).
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Last modified: 2 November 1996 by Denise Moore