Lloyd N. Trefethen
|Born||Lloyd Nicholas Trefethen
30 August 1955 
|Thesis||Wave Propagation and Stability for Finite Difference Schemes (1982)|
|Doctoral advisor||Joseph E. Oliger|
|Known for||Embree–Trefethen constant|
|Children||one son, one daughter|
(Lloyd) Nicholas Trefethen, FRS (born 30 August 1955) is professor of numerical analysis and head of the Numerical Analysis Group at the Mathematical Institute, University of Oxford.
Trefethen obtained his bachelor's degree from Harvard University in 1977 and his master's from Stanford University in 1980. His PhD was on Wave Propagation and Stability for Finite Difference Schemes supervised by Joseph E. Oliger at Stanford University.
Career and research
Following his PhD, Trefethen went on to work at the Courant Institute of Mathematical Sciences in New York, Massachusetts Institute of Technology, and Cornell University, before being appointed to a chair at the University of Oxford and a Fellowship of Balliol College, Oxford.
As of 2009[update], he has published around 125 journal papers spanning a wide range of areas within numerical analysis and applied mathematics, including non-normal eigenvalue problems and applications, spectral methods for differential equations, numerical linear algebra, fluid mechanics, computational complex analysis, and approximation theory. He is perhaps best known for his work on pseudospectra of non-normal matrices and operators. This work covers theoretical aspects as well as numerical algorithms, and applications including fluid mechanics, numerical solution of partial differential equations, numerical linear algebra, shuffling of cards, random matrices, differential equations and lasers. Trefethen is currently an ISI highly cited researcher.
Trefethen has written a number of books on numerical analysis including Numerical Linear Algebra with David Bau, Spectral Methods in MATLAB, Schwarz–Christoffel Mapping with Tobin Driscoll, and Spectra and Pseudospectra: The Behavior of Nonnormal Matrices and Operators with Mark Embree. He has recently been heavily involved in the creation and development of the MATLAB-based Chebfun software project.
- Numerical Linear Algebra (1997) with David Bau
- Spectral Methods in Matlab (2000)
- "Hydrodynamic stability without eigenvalues"  with Anne Trefethen, Satish Reddy, and Tobin Driscoll
- "Pseudospectra of linear operators" SIAM Review (1997)
Awards and honours
Trefethen was the first winner of the Leslie Fox Prize for Numerical Analysis. He is a fellow of the American Mathematical Society, and a member of the National Academy of Engineering in the United States. Trefethen was elected a Fellow of the Royal Society (FRS) in 2005, his certificate of election reads:
|“||Nick Trefethen is distinguished for his many seminal contributions to Numerical Analysis and its applications in Applied Mathematics and in Engineering Science. His research spans theory, algorithms, software and physical applications, particularly involving eigenvalues, pseudospectra - a concept which he introduced - and dynamics. He has an international reputation for his work on nonnormal matrices and operators. He has also made major contributions to finite difference and spectral methods for partial differential equations, numerical linear algebra, and complex analysis. His monograph Numerical Linear Algebra (SIAM, 1997) is one of the SIAM's best selling books and has already been through five printings.||”|
- TREFETHEN, Prof. Lloyd Nicholas, (Nick). Who's Who. 2015 (online Oxford University Press ed.). A & C Black, an imprint of Bloomsbury Publishing plc. (subscription required)
- "New directions in Numerical Computation, 25-28 August 2015: In Celebration of Nick Trefethen's 60th birthday". University of Oxford. Archived from the original on 2015-04-04. line feed character in
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- Lloyd N. Trefethen at the Mathematics Genealogy Project
- Banjai, Lehel. (2003). Computation of conformal maps by fast multipole method accelerated Schwarz-Christoffel transformation (PhD thesis). University of Oxford.
- Birkisson, Asgeir (2013). Numerical solution of nonlinear boundary value problems for ordinary differential equations in the continuous framework (PhD thesis). University of Oxford.
- Pachon, Ricardo (2010). Algorithms for polynomial and rational approximation (PhD thesis). University of Oxford.
- Townsend, Alex (2014). Computing with functions in two dimensions (PhD thesis). University of Oxford.
- Embree, M.; Trefethen, L. N. (1999). "Growth and decay of random Fibonacci sequences" (PDF). Proceedings of the Royal Society A: Mathematical, Physical and Engineering Sciences. 455 (1987): 2471. Bibcode:1999RSPSA.455.2471T. doi:10.1098/rspa.1999.0412.
- "Certificate of candidature and election: Trefethen, Lloyd Nicholas, EC/2005/40". London: The Royal Society. Archived from the original on 2014-01-22.
- Trefethen, Lloyd Nicholas (1982). Wave Propagation and Stability for Finite Difference Schemes (PhD thesis). Stanford University. OCLC 9136203.
- Lloyd N. Trefethen's publications indexed by the Scopus bibliographic database, a service provided by Elsevier. (subscription required)
- Lloyd N. Trefethen's publications indexed by Google Scholar, a service provided by Google
- Lloyd N. Trefethen at DBLP Bibliography Server
- Nachtigal, N. L. M.; Reddy, S. C.; Trefethen, L. N. (1992). "How Fast are Nonsymmetric Matrix Iterations?". SIAM Journal on Matrix Analysis and Applications. 13 (3): 778. doi:10.1137/0613049.
- Lloyd N. Trefethen from the Association for Computing Machinery (ACM) Digital Library
- "SNC '07 Invited Speakers". Retrieved 2008-04-26.
- "Nick Trefethen publication list".
- "T – Research Analytics – Thomson Reuters". Highlycited.com. 2011-09-15. Retrieved 2013-02-12.
- Stewart, G. W. (1999). "Review: Numerical linear algebra, by L. N. Trefethen and D. Bau". Math. Comp. 68: 453–454. doi:10.1090/S0025-5718-99-01069-8.
- Higham, Nicholas J. (2007). "Review: Spectra and pseudospectra: the behavior of nonnormal matrices and operators, by L. N. Trefethen and M. Embree". Bull. Amer. Math. Soc. (N.S.). 44 (2): 277–284. doi:10.1090/s0273-0979-06-01128-1.
- Trefethen, L. N.; Trefethen, A. E.; Reddy, S. C.; Driscoll, T. A. (1993). "Hydrodynamic Stability Without Eigenvalues". Science. 261 (5121): 578–584. doi:10.1126/science.261.5121.578. PMID 17758167.
- List of Fellows of the American Mathematical Society, retrieved 2013-08-27.
- "List of LMS prize winners". London Mathematical Society. Retrieved 25 November 2014.