Nick Trefethen | |
---|---|
Born | Lloyd Nicholas Trefethen 30 August 1955 [1] [2] |
Alma mater | |
Known for | Embree–Trefethen constant [3] |
Spouses | |
Children | one son, one daughter [1] |
Awards |
|
Scientific career | |
Fields | Numerical analysis |
Institutions | |
Thesis | Wave Propagation and Stability for Finite Difference Schemes (1982) |
Doctoral advisor | Joseph E. Oliger [5] |
Doctoral students | Alan Edelman |
Website | people |
Lloyd Nicholas Trefethen FRS [4] (born 30 August 1955) is an American mathematician, professor of numerical analysis and until 2023 head of the Numerical Analysis Group at the Mathematical Institute, University of Oxford. [6] [7] [8] [9]
Trefethen was born 30 August 1955 in Boston, Massachusetts, [10] the son of mechanical engineer Lloyd M. Trefethen and codebreaker, poet, teacher and editor Florence Newman Trefethen. [1] Trefethen attended Phillips Exeter Academy.
He obtained his bachelor's degree from Harvard College 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. [5] [11] [12]
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. [13]
His publications span 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. [14] 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. [15]
Trefethen has written a number of books on numerical analysis including Numerical Linear Algebra [16] with David Bau, Spectral Methods in MATLAB, Schwarz–Christoffel Mapping with Tobin Driscoll, and Spectra and Pseudospectra: The Behavior of Nonnormal Matrices and Operators [17] with Mark Embree. [3] He is the leader of the MATLAB-based Chebfun software project.
In 2013 he proposed a new formula to calculate the BMI of a person: [18] [19]
(International System of Units)
Trefethen was the first winner of the Leslie Fox Prize for Numerical Analysis. In 1998 he was an Invited Speaker of the International Congress of Mathematicians in Berlin. [20] He is a fellow of the American Mathematical Society, [21] 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, [4] and 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. [4]
In 2010 Trefethen was awarded the Gold Medal of the Institute of Mathematics and its Applications in recognition of his "outstanding contributions to mathematics and its applications over a period of years". [22] In 2013 Trefethen was awarded the Naylor Prize and lectureship in Applied Mathematics from the London Mathematical Society. [23] He was awarded the George Pólya Prize for Mathematical Exposition in 2017 and the John von Neumann Prize in 2020 by SIAM.
Trefethen has one son and one daughter from his first marriage to Anne Elizabeth Trefethen (née Daman). [1] He is currently married to Kate McLoughlin, a professor of English Literature at Oxford.
Linear algebra is the branch of mathematics concerning linear equations such as:
Numerical analysis is the study of algorithms that use numerical approximation for the problems of mathematical analysis. It is the study of numerical methods that attempt to find approximate solutions of problems rather than the exact ones. Numerical analysis finds application in all fields of engineering and the physical sciences, and in the 21st century also the life and social sciences like economics, medicine, business and even the arts. Current growth in computing power has enabled the use of more complex numerical analysis, providing detailed and realistic mathematical models in science and engineering. Examples of numerical analysis include: ordinary differential equations as found in celestial mechanics, numerical linear algebra in data analysis, and stochastic differential equations and Markov chains for simulating living cells in medicine and biology.
In the mathematical discipline of linear algebra, the Schur decomposition or Schur triangulation, named after Issai Schur, is a matrix decomposition. It allows one to write an arbitrary complex square matrix as unitarily similar to an upper triangular matrix whose diagonal elements are the eigenvalues of the original matrix.
In mathematics, operator theory is the study of linear operators on function spaces, beginning with differential operators and integral operators. The operators may be presented abstractly by their characteristics, such as bounded linear operators or closed operators, and consideration may be given to nonlinear operators. The study, which depends heavily on the topology of function spaces, is a branch of functional analysis.
Computational science, also known as scientific computing, technical computing or scientific computation (SC), is a division of science that uses advanced computing capabilities to understand and solve complex physical problems. This includes
In linear algebra, an eigenvector or characteristic vector is a vector that has its direction unchanged by a given linear transformation. More precisely, an eigenvector, , of a linear transformation, , is scaled by a constant factor, , when the linear transformation is applied to it: . It is often important to know these vectors in linear algebra. The corresponding eigenvalue, characteristic value, or characteristic root is the multiplying factor .
In mathematics, the pseudospectrum of an operator is a set containing the spectrum of the operator and the numbers that are "almost" eigenvalues. Knowledge of the pseudospectrum can be particularly useful for understanding non-normal operators and their eigenfunctions.
Gene Howard Golub, was an American numerical analyst who taught at Stanford University as Fletcher Jones Professor of Computer Science and held a courtesy appointment in electrical engineering.
Numerical linear algebra, sometimes called applied linear algebra, is the study of how matrix operations can be used to create computer algorithms which efficiently and accurately provide approximate answers to questions in continuous mathematics. It is a subfield of numerical analysis, and a type of linear algebra. Computers use floating-point arithmetic and cannot exactly represent irrational data, so when a computer algorithm is applied to a matrix of data, it can sometimes increase the difference between a number stored in the computer and the true number that it is an approximation of. Numerical linear algebra uses properties of vectors and matrices to develop computer algorithms that minimize the error introduced by the computer, and is also concerned with ensuring that the algorithm is as efficient as possible.
Mark Embree is professor of computational and applied mathematics at Virginia Tech in Blacksburg, Virginia. Until 2013, he was a professor of computational and applied mathematics at Rice University in Houston, Texas.
Nicholas John Higham FRS was a British numerical analyst. He was Royal Society Research Professor and Richardson Professor of Applied Mathematics in the Department of Mathematics at the University of Manchester.
Leslie Fox was a British mathematician noted for his contribution to numerical analysis.
In mathematics, the joint spectral radius is a generalization of the classical notion of spectral radius of a matrix, to sets of matrices. In recent years this notion has found applications in a large number of engineering fields and is still a topic of active research.
Chebfun is a free/open-source 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. Thus, for example, whereas the SUM command in MATLAB adds up the elements of a vector, the SUM command in Chebfun evaluates a definite integral. Similarly the backslash command in MATLAB becomes a Chebfun command for solving differential equations.
The following is a timeline of numerical analysis after 1945, and deals with developments after the invention of the modern electronic computer, which began during Second World War. For a fuller history of the subject before this period, see timeline and history of mathematics.
Alan Stuart Edelman is an American mathematician and computer scientist. He is a professor of applied mathematics at the Massachusetts Institute of Technology (MIT) and a Principal Investigator at the MIT Computer Science and Artificial Intelligence Laboratory (CSAIL) where he leads a group in applied computing. In 2004, he founded a business called Interactive Supercomputing which was later acquired by Microsoft. Edelman is a fellow of American Mathematical Society (AMS), Society for Industrial and Applied Mathematics (SIAM), Institute of Electrical and Electronics Engineers (IEEE), and Association for Computing Machinery (ACM), for his contributions in numerical linear algebra, computational science, parallel computing, and random matrix theory. He is one of the creators of the technical programming language Julia.
Beresford Neill Parlett is an English applied mathematician, specializing in numerical analysis and scientific computation.
In matrix analysis, Kreiss matrix theorem relates the so-called Kreiss constant of a matrix with the power iterates of this matrix. It was originally introduced by Heinz-Otto Kreiss to analyze the stability of finite difference methods for partial difference equations.
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