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
mathematics. Much of my work within this area concerns nonnormal
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 Laplace eigenvalue
problems on polygons such as the problem underlying the question, "Can
one hear the shape of a drum?".
Recent Ph.D. KimChuan Toh and I developed new algorithms and results
concerning convergence of largescale 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 "cutoff" phenomenon in
shuffling a deck of cards.
Ph.D. student Vicki Howle and I are investigating questions of
eigenvalues, pseudoeigenvalues, 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 MPIbased extension of MATLAB that enables MATLAB
users to run jobs conveniently on multiple processors of an SP2 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
 Nonnormality, 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 nonnormality 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 nonnormality 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), 115 (with K. Toh).
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