Lloyd Nicholas Trefethen
Encyclopedia
Lloyd Nicholas Trefethen FRS is professor of numerical analysis
and head of the Numerical Analysis Group in the Mathematical Institute
at the University of Oxford
.
Nick Trefethen (as he is known) gained his bachelor's degree from Harvard
in 1977 and his master's from Stanford
in 1980. His PhD thesis at Stanford in 1982 was entitled Wave Propagation and Stability for Finite Difference Schemes. He went on to work at the Courant Institute in New York, MIT and Cornell
, before being appointed to a chair at Oxford
and a Fellowship of Balliol College.
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.
Trefethen was the first winner of the Leslie Fox Prize for Numerical Analysis
, and as well as being a Fellow of the Royal Society
he is a member of the National Academy of Engineering
in the USA.
Numerical analysis
Numerical analysis is the study of algorithms that use numerical approximation for the problems of mathematical analysis ....
and head of the Numerical Analysis Group in the Mathematical Institute
The Mathematical Institute, University of Oxford
The Mathematical Institute is the mathematics department at the University of Oxford, England. It forms one of the ten departments of the Mathematical, Physical and Life Sciences Divisional Board in the University....
at the University of Oxford
University of Oxford
The University of Oxford is a university located in Oxford, United Kingdom. It is the second-oldest surviving university in the world and the oldest in the English-speaking world. Although its exact date of foundation is unclear, there is evidence of teaching as far back as 1096...
.
Nick Trefethen (as he is known) gained his bachelor's degree from Harvard
Harvard University
Harvard University is a private Ivy League university located in Cambridge, Massachusetts, United States, established in 1636 by the Massachusetts legislature. Harvard is the oldest institution of higher learning in the United States and the first corporation chartered in the country...
in 1977 and his master's from Stanford
Stanford University
The Leland Stanford Junior University, commonly referred to as Stanford University or Stanford, is a private research university on an campus located near Palo Alto, California. It is situated in the northwestern Santa Clara Valley on the San Francisco Peninsula, approximately northwest of San...
in 1980. His PhD thesis at Stanford in 1982 was entitled Wave Propagation and Stability for Finite Difference Schemes. He went on to work at the Courant Institute in New York, MIT and Cornell
Cornell University
Cornell University is an Ivy League university located in Ithaca, New York, United States. It is a private land-grant university, receiving annual funding from the State of New York for certain educational missions...
, before being appointed to a chair at Oxford
Oxford
The city of Oxford is the county town of Oxfordshire, England. The city, made prominent by its medieval university, has a population of just under 165,000, with 153,900 living within the district boundary. It lies about 50 miles north-west of London. The rivers Cherwell and Thames run through...
and a Fellowship of Balliol College.
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
Numerical linear algebra
Numerical linear algebra is the study of algorithms for performing linear algebra computations, most notably matrix operations, on computers. It is often a fundamental part of engineering and computational science problems, such as image and signal processing, Telecommunication, computational...
, fluid mechanics
Fluid mechanics
Fluid mechanics is the study of fluids and the forces on them. Fluid mechanics can be divided into fluid statics, the study of fluids at rest; fluid kinematics, the study of fluids in motion; and fluid dynamics, the study of the effect of forces on fluid motion...
, computational complex analysis
Complex analysis
Complex analysis, traditionally known as the theory of functions of a complex variable, is the branch of mathematical analysis that investigates functions of complex numbers. It is useful in many branches of mathematics, including number theory and applied mathematics; as well as in physics,...
, and approximation theory. He is perhaps best known for his work on pseudospectra
Pseudospectrum
In mathematics, the pseudospectrum of an operator is a set containing the spectrum of the operator and the numbers that are "almost" eigenvalues...
of non-normal matrices
Normal matrix
A complex square matrix A is a normal matrix ifA^*A=AA^* \ where A* is the conjugate transpose of A. That is, a matrix is normal if it commutes with its conjugate transpose.If A is a real matrix, then A*=AT...
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
ISI highly cited researcher
ISI Highly Cited is a database of "highly cited researchers"—scientific researchers whose publications are most often cited in academic journals over the past decade, published by the Institute for Scientific Information...
.
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
Mark Embree
Mark Embree is professor of computational and applied mathematics at Rice University in Houston, Texas.His main research interests are Krylov subspace methods, non-normal operators and spectral perturbation theory, Toeplitz matrices, random matrices, and damped wave operators.Mark Embree was...
. He has recently been heavily involved in the creation and development of the MATLAB
MATLAB
MATLAB is a numerical computing environment and fourth-generation programming language. Developed by MathWorks, MATLAB allows matrix manipulations, plotting of functions and data, implementation of algorithms, creation of user interfaces, and interfacing with programs written in other languages,...
-based Chebfun
Chebfun
Chebfun is a freely available software system written in MATLAB for numerical computation with functions of a real variable. It is based on the idea of overloading MATLAB's commands for vectors and matrices to analogous commands for functions and operators...
software project.
Trefethen was the first winner of the Leslie Fox Prize for Numerical Analysis
Leslie Fox Prize for Numerical Analysis
The Leslie Fox Prize for Numerical Analysis of the Institute of Mathematics and its Applications is a biennial prize established in 1985 by the IMA in honour of mathematician Leslie Fox . The prize honours "young numerical analysts worldwide" , and applicants submit papers for review...
, and as well as being a Fellow of the Royal Society
Royal Society
The Royal Society of London for Improving Natural Knowledge, known simply as the Royal Society, is a learned society for science, and is possibly the oldest such society in existence. Founded in November 1660, it was granted a Royal Charter by King Charles II as the "Royal Society of London"...
he is a member of the National Academy of Engineering
National Academy of Engineering
The National Academy of Engineering is a government-created non-profit institution in the United States, that was founded in 1964 under the same congressional act that led to the founding of the National Academy of Sciences...
in the USA.
Partial bibliography
- Numerical Linear Algebra (1997) with David Bau
- Spectral Methods in Matlab (2000)
- "Hydrodynamic stability without eigenvalues" Science (1993) with Anne Trefethen, Satish Reddy, and Tobin Driscoll
- "Pseudospectra of linear operators" SIAM Review (1997)