# Nick Trefethen

Lloyd Nicholas Trefethen FRS[4] (born 30 August 1955) is a British mathematician, professor of numerical analysis and head of the Numerical Analysis Group at the Mathematical Institute, University of Oxford.[6][7][8][9]

Nick Trefethen

Born
Lloyd Nicholas Trefethen

30 August 1955[1][2]
Alma mater
Known forEmbree–Trefethen constant[3]
Spouse(s)
• Anne Trefethen (née Daman) (m. 19882008)
• Kate McLoughlin (m. 2011)
Childrenone son, one daughter[1]
Awards
Scientific career
FieldsNumerical analysis
Institutions
ThesisWave Propagation and Stability for Finite Difference Schemes (1982)
Doctoral studentsAlan Edelman
Websitepeople.maths.ox.ac.uk/trefethen

## Education

Trefethen was born 30 August 1955 in Boston, Massachusetts,[10] the son of mechanical engineer Lloyd M. Trefethen and codebreaker, poet, and English professor Florence Newman Trefethen.[1]

He 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.[5][11][12]

## 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.[13]

As of 2018, he has published around 140 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.[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 has recently been heavily involved in the creation and development of the MATLAB-based Chebfun software project.

In 2013 he proposed a new formula to calculate the BMI of a person:[18][19]

${\displaystyle {\text{BMI}}=1.3\times {\frac {{\text{weight}}\,\,\,\,}{{\text{height}}^{2.5}}}}$

### Notable publications

• Numerical Linear Algebra (1997) with David Bau
• Spectral Methods in Matlab (2000)
• "Hydrodynamic stability without eigenvalues"[20] 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. In 1998 he was an Invited Speaker of the International Congress of Mathematicians in Berlin.[21] He is a fellow of the American Mathematical Society,[22] 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] 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".[23] In 2013 Trefethen was awarded the Naylor Prize and lectureship in Applied Mathematics from the London Mathematical Society.[24]

## Personal life

Trefethen has one son and one daughter from his first marriage to Anne Elizabeth Trefethen (née Daman).[1]

## References

1. "TREFETHEN, Prof. Lloyd Nicholas, (Nick)". Who's Who. ukwhoswho.com. 2015 (online Oxford University Press ed.). A & C Black, an imprint of Bloomsbury Publishing plc. (subscription or UK public library membership required) (subscription required)
2. "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 4 April 2015.
3. 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. CiteSeerX 10.1.1.33.1658. doi:10.1098/rspa.1999.0412.
4. "Certificate of candidature and election: Trefethen, Lloyd Nicholas, EC/2005/40". London: The Royal Society. Archived from the original on 22 January 2014.
5. Nick Trefethen's publications indexed by the Scopus bibliographic database. (subscription required)
6. Nick Trefethen publications indexed by Google Scholar
7. Lloyd N. Trefethen at DBLP Bibliography Server
8. 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. CiteSeerX 10.1.1.210.62. doi:10.1137/0613049.
9. American Men & Women of Science: Physical and Biological Sciences. Jaques Cattell Press. (16th ed.). New York: Bowker. 1986. p. 184. ISBN 0835222217. OCLC 13680380.CS1 maint: others (link)
10. Trefethen, Lloyd Nicholas (1982). Wave Propagation and Stability for Finite Difference Schemes (PhD thesis). Stanford University. OCLC 9136203.
11. Nick Trefethen author profile page at the ACM Digital Library
12. "SNC '07 Invited Speakers". Retrieved 26 April 2008.
13. "Nick Trefethen publication list".
14. "T – Research Analytics – Thomson Reuters". Highlycited.com. 15 September 2011. Retrieved 12 February 2013.
15. Stewart, G. W. (1999). "Review: Numerical linear algebra, by L. N. Trefethen and D. Bau". Math. Comp. 68 (225): 453–454. doi:10.1090/S0025-5718-99-01069-8.
16. 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.
17. "New BMI (New Body Mass Index)".
18. Stephenson, Wesley (29 January 2013). "Does the BMI need correcting?". BBC News.
19. Trefethen, L. N.; Trefethen, A. E.; Reddy, S. C.; Driscoll, T. A. (1993). "Hydrodynamic Stability Without Eigenvalues". Science. 261 (5121): 578–584. Bibcode:1993Sci...261..578T. doi:10.1126/science.261.5121.578. PMID 17758167.
20. Trefethen, Lloyd N.; Driscoll, Tobin A. (1998). "Schwarz-Christoffel mapping in the computer era". Doc. Math. (Bielefeld) Extra Vol. ICM Berlin, 1998, vol. III. pp. 533–542.
21. List of Fellows of the American Mathematical Society. Retrieved 27 August 2013.
22. "IMA Gold Medal". Retrieved 16 May 2018. Institute of Mathematics and its Applications
23. "List of LMS prize winners". London Mathematical Society. Retrieved 25 November 2014.