Professor L N Trefethen FRS: Publications

1 The chebop system for automatic solution of differential equations
T. A. Driscoll, F. Bornemann and L. N. Trefethen
BIT Numerical Mathematics (2008), Online First.
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2 Numerical analysis
L. N. Trefethen
In W. T. Gowers, ed., Princeton Companion to Mathematics, Princeton U. Press. 2008.
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3
Computing Aα, log(A), and related matrix functions by contour integrals
N. Hale, N. J. Higham and L. N. Trefethen
SIAM J. Numer. Anal., Vol. 46, No. 5, pp. 2505-2523. 2008.
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4
G.H. Hardy, applied mathematician
L. N. Trefethen
SIAM News, Vol. 41 / No. 3, pp. 1+3, April 2008.
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5
New quadrature formulas from conformal maps
N. Hale and L. N. Trefethen
SIAM J. Numer. Anal., Vol. 46, No. 2, pp. 930-948. 2008.
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6
Is Gauss quadrature better than Clenshaw-Curtis?
L. N. Trefethen
SIAM Review 50, No. 1, pp. 67-87, 2008.
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7
Obituary Gene H. Golub (1932-2007)
L. N. Trefethen
Nature, Vol. 450, p. 962, 13 Dec. 2007.
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8
Evaluating matrix functions for exponential integrators via Carathéodory-Fejér approximation and contour integrals
T. Schmelzer and L. N. Trefethen
ETNA, Volume 29, pp. 1-18, 2007.
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9
The kink phenomenon in Fejér and Clenshaw-Curtis quadrature
J. A. C. Weideman and L. N. Trefethen
Numer. Math. (2007) 107: 707-727.
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10
Computing numerically with functions instead of numbers
L. N. Trefethen
Math. Comput. Sci. 1 (2007), pp. 9-19.
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11
Computing the gamma function using contour integrals and rational approximations
T. Schmelzer and L. N. Trefethen
SIAM J. Numer. Anal., Vol. 45 (2007), No. 2, pp. 558-571.
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12
Parabolic and hyperbolic contours for computing the Bromwich integral
J. A. C. Weideman and L. N. Trefethen
Math. Comp. 76 (2007), 1341-1356.
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13
A rational spectral collocation method with adaptively transformed Chebyshev grid points
T.-W. Tee and L. N. Trefethen
SIAM J. Sci. Comp., Vol. 28 (2006), No. 5, pp. 1798-1811.
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14 Talbot quadratures and rational approximations
L. N. Trefethen, J. A. C. Weideman and T. Schmelzer
BIT Numerical Mathematics (2006) 46, pp. 653-670.
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15 Computed eigenmodes of planar regions
L. N. Trefethen and T. Betcke
In N. Chernov, et al., eds., Recent Advances in Differential Equations and Mathematical Physics, Contemp. Math. 412, Amer. Math. Soc., 2006, pp. 297-314.
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16 Spectra and Pseudospectra: The Behavior of Nonnormal Matrices and Operators
L. N. Trefethen and Mark Embree
xviii+606 pages. Princeton U. Press, 2005.
(Winner of Honorable Mention, 2005 Awards for Excellence in Professional/Scholar Publishing in Mathematics and Statistics, Association of American Publishers.)
Book
17 Ten Digit Algorithms
L. N. Trefethen
Numerical Analysis Report 05/13, Oxford University, 2005.
(From the 2005 A. R. Mitchell Lecture, Dundee.)
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18 Wave packet pseudomodes of variable coefficient differential operators
L. N. Trefethen
Proc. Roy. Soc. Lond. A 561 (2005), 3099-3122.
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19 Reviving the method of particular solutions
T. Betcke and L. N. Trefethen
SIAM Review 47 (2005), 469-491.
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20 Fourth-order time-stepping for stiff PDEs
A. K. Kassam and L. N. Trefethen
SIAM J. Sci. Comp. 26 (2005), 1214-1233.
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21 Computations of eigenvalue avoidance in planar domains
T. Betcke and L. N. Trefethen
Proc. Appl. Math. Mech. 4 (2004), 634-635.
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22
Wave packet pseudomodes of twisted Toeplitz matrices
L. N. Trefethen and S. J. Chapman
Comm. Pure Appl. Math. 57 (2004), 1233-1264.
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23 An extension of Matlab to continuous functions and operators
Z. Battles and L. N. Trefethen
SIAM J. Sci. Comp. 25 (2004), 1743-1770.
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24 Barycentric Lagrange interpolation
J.-P. Berrut and L. N. Trefethen
SIAM Review 46 (2004), 501-517.
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25 An American at Oxford
L. N. Trefethen
Oxford Magazine, May 2003.
(This essay was discussed in the Times Higher Education Supplement and elsewhere.)
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26 Linearized pipe flow to Reynolds number 107
A. Meseguer and L. N. Trefethen
J. Comp. Phys. 186 (2003), 178-197.
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27 A multipole method for Schwarz-Christoffel mapping of polygons with thousands of sides
L. Banjai and L. N. Trefethen
SIAM J. Sci. Comp. 25 (2003), 1042-1065.
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28 Schwarz-Christoffel Mapping
Tobin A. Driscoll and L. N. Trefethen
xvi+132 pages. Cambridge U. Press, 2002.
Book
29 Pseudospectra of rectangular matrices
T. G. Wright and L. N. Trefethen
IMA J. Numer. Anal. 22 (2002), 501-519.
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30 Piecewise continuous Toeplitz matrices and operators: slow approach to infinity
A. Böttcher, M. Embree and L. N. Trefethen
SIAM J. Matrix Anal. Applics. 24 (2002), 484-489.
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31 Chastened Challenge Sponsor: "I Misjudged"
L. N. Trefethen
SIAM News, Vol. 35, No. 6, July/Aug. 2002.
(follow-up article).
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32
A hundred-dollar, hundred-digit challenge
L. N. Trefethen
SIAM News, Vol. 35, No. 1, Jan./Feb. 2002.
(This led to two books by Bornemann et al.)
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33 Numerical solution of the omitted area problem of univalent function theory
L. Banjai and L. N. Trefethen
Computational Methods and Function Theory 1 (2001), 259-273.
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34 Spectra, pseudospectra and localization for random bidiagonal matrices
L. N. Trefethen, M. Contedini and M. Embree
Comm. Pure Appl. Math. 54 (2001), 595-623.
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35 Large-scale computation of pseudospectra using ARPACK and eigs
T. G. Wright and L. N. Trefethen
SIAM J. Sci. Comput. 23 (2001), 591-605.
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36 Generalizing eigenvalue theorems to pseudospectra theorems
M. Embree and L. N. Trefethen
SIAM J. Sci. Comput. 23 (2001), 583-590.
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37 Eigenvalues and musical instruments
V. E. Howle and L. N. Trefethen
J. Comp. Appl. Math. 135 (2001), 23-40.
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38 Computing Lyapunov constants for random recurrences with smooth coefficients
T. G. Wright and L. N. Trefethen
J. Comp. Appl. Math. 132 (2001), 331-340.
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39 Spectral Methods in MATLAB
L. N. Trefethen
xviii+165 pages. SIAM, 2000.
Book
40 Pseudospectra Gateway.
M. Embree and L. N. Trefethen
Web Site: http://www.comlab.ox.ac.uk/pseudospectra, 2000.
Web pages
41 Threshold amplitudes for transition to turbulence in a pipe
L. N. Trefethen, S. J. Chapman, D. S. Henningson, A. Meseguer, T. Mullin, and F. T. M. Nieuwstadt
Num. Anal. Group Report NA 00/17, Oxford U. Computing Lab., 2000.
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42
Predictions for scientific computing fifty years from now
L. N. Trefethen
Mathematics Today, April 2000, 53-57.
(This essay won the Catherine Richards Prize of the Inst. for Maths. and Applics., 2000.)
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43 How many shuffles to randomize a deck of cards?
L. N. Trefethen and L. M. Trefethen
Proc. Roy. Soc. London A 456 (2000), 2561-2568.
(This article led to dozens of press reports in newspapers, magazines, radio and television.)
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44 Growth and decay of random Fibonacci sequences
M. Embree and L. N. Trefethen
Proc. Royal Soc. Lond. A 455 (1999), 2471-2485.

45 Large-amplitude transient growth in the linear evolution of equatorial spread F with a sheared zonal flow
J. P. Flaherty and C. E. Seyler and L. N. Trefethen
J. Geophys. Res. 104 (1999), 6843.

46 Spectra and pseudospectra for pipe Poiseuille flow
A. E. Trefethen, L. N. Trefethen and P. J. Schmid
Comp. Meth. Appl. Mech. Engr. 1926 (1999), 413-420.
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47 Computation of pseudospectra
L. N. Trefethen
Acta Numerica 8 (1999), 247-295.
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48 Spectra and pseudospectra
L. N. Trefethen
In M. Ainsworth, J. Levesley, and M. Marletta, The Graduate Student's Guide to Numerical Analysis, Springer, 1999, pp. 217-250.
Chapter in book
49 The Kreiss matrix theorem on a general complex domain
K.-C. Toh and L. N. Trefethen
SIAM J. Matrix Anal. Applics. 21 (1999), 145-165.
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50 Green's functions for multiply connected domains via conformal mapping
M. Embree and L. N. Trefethen
SIAM Review 41 (1999), 721-744.
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51 Schwarz-Christoffel mapping in the computer era
T. A. Driscoll and L. N. Trefethen
Proc. Int. Congress Mathematicians 1998, pp. 533-542.
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52
From potential theory to matrix iterations in six steps
T. A. Driscoll, K.-C. Toh and L. N. Trefethen
SIAM Review 40 (1998), 547-578.
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53 Condition numbers of random triangular matrices
D. Viswanath and L. N. Trefethen
SIAM J. Matrix Anal. Applics. 19 (1998), 564-581.
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54 Maxims about numerical mathematics, computers, science, and life
L. N. Trefethen
SIAM News v. 31, no. 1 (1998), p. 4.
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55 The Chebyshev polynomials of a matrix
K.-C. Toh and L. N. Trefethen
SIAM J. Matrix Anal. Applics. 20 (1998), 400-419.
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56 A numerical analyst looks at the 'cutoff phenomenon' in card shuffling and other Markov chains
G. F. Jonsson and L. N. Trefethen
Dundee proceedings, 1997; also in D. F. Griffiths, D. J. Higham, and G. A. Watson, eds., Numerical Analysis 1997, Addison Wesley Longman, 1998.
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57 Numerical Linear Algebra
L. N. Trefethen and David Bau III
xii+361 pages. SIAM, 1997.
(SIAM's bestselling book of the past decade.)
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58 Pseudospectra of linear operators
L. N. Trefethen
ICIAM '95: Proceedings of the Third International Congress on Industrial and Applied Mathematics, Akademie-Verlag, Berlin, 1996, pp. 401-434; also SIAM Review 39 (1997), 383-406.
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59 Low-dimensional models of subcritical transition to turbulence
J. S. Baggett and L. N. Trefethen
Physics of Fluids 9 (1997), 1043-1053.
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60 Finite Difference and Spectral Methods for Ordinary and Partial Differential Equations
L. N. Trefethen
x+315 pages. Graduate textbook, unpublished, 1996,
available at http://web.comlab.ox.ac.uk/oucl/work/nick.trefethen/pdetext.html
Book
61 MultiMATLAB: MATLAB on multiple processors
A. E. Trefethen, V. S. Menon, C.-C. Chang, G. J. Czajkowski, C. Myers, and L. N. Trefethen
Tech. Rep. CTC96TR293, Cornell Theory Center, 1996.
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62
Matrix behaviour, unitary reducibility, and Hadamard products
D. Viswanath and L. N. Trefethen
Tech. Rep. TR96-1596, Dept. of Comp. Sci., Cornell U., July, 1996.
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63 Pseudospectra for the wave operator with an absorbing boundary
T. A. Driscoll and L. N. Trefethen
J. Comp. Appl. Math. 69 (1996), 125-142.
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64 Calculation of pseudospectra by the Arnoldi iteration
K.-C. Toh and L. N. Trefethen
SIAM J. Sci. Comp. 17 (1996), 1-15.
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65 A mostly linear model of transition to turbulence
J. S. Baggett, T. A. Driscoll and L. N. Trefethen
Physics of Fluids 7 (1995), 833-838.
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66 Do the pseudospectra of a matrix determine its behavior?
A. Greenbaum and L. N. Trefethen
unpublished technical report, 1995.
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67 Pseudospectra of the convection-diffusion operator
S. C. Reddy and L. N. Trefethen
SIAM J. Appl. Math. 54 (1994), 1634-1649.
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68 Pseudozeros of polynomials and pseudospectra of companion matrices
K.-C. Toh and L. N. Trefethen
Numer. Math. 68 (1994), 403-425.
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69 GMRES/CR and Arnoldi/Lanczos as matrix approximation problems
A. Greenbaum and L. N. Trefethen
SIAM J. Sci. Comput. 15 (1994), 359-368.
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70 From the Buffon needle problem to the Kreiss Matrix Theorem
E. Wegert and L. N. Trefethen
Amer. Math. Monthly 101 (1994), 132-139.
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71 Numerical construction of conformal maps
L. N. Trefethen
Appendix to E. B. Saff and A. D. Snider, Fundamentals of Complex Analysis, 2nd ed., Prentice Hall, 1993.

72
Hydrodynamic stability without eigenvalues
L. N. Trefethen, A. E. Trefethen, S. C. Reddy, and T. A. Driscoll
Science 261 (1993), 578-584.
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73 Stiffness of ODEs
D. J. Higham and L. N. Trefethen
BIT 33 (1993), 285-303.
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74 The definition of numerical analysis
L. N. Trefethen
SIAM News 25, 6 Nov. 1992; reprinted in Bull. Inst. Maths. and Applics., 1993 and again as an appendix to L. N. Trefethen and D. A. Bau, III, Numerical Linear Algebra, SIAM, 2000.
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75 Pseudospectra of matrices
L. N. Trefethen
In D. F. Griffiths and G. A. Watson, eds., Numerical Analysis 1991, Longman, 1992.
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76 Eigenvalues and pseudo-eigenvalues of Toeplitz matrices
L. Reichel and L. N. Trefethen
Lin. Alg. Applics. 162-164 (1992), 153-185.

77 How fast are nonsymmetric matrix iterations?
N. M. Nachtigal, S. C. Reddy and L. N. Trefethen
SIAM J. Matrix Anal. Applics. 13 (1992), 778-795.
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78 A hybrid GMRES algorithm for nonsymmetric linear systems
N. M. Nachtigal, L. Reichel and L. N. Trefethen
SIAM J. Matrix Anal. Applics. 13 (1992), 796-825.
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79 Stability of the method of lines
S. C. Reddy and L. N. Trefethen
Numer. Math. 62 (1992), 235-267.
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80 Two results on polynomial interpolation in equally spaced points
L. N. Trefethen and J. A. C. Weideman
J. Approx. Theory 65 (1991), 247-260.
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81 Lax-stability of fully discrete spectral methods via stability regions and pseudo-eigenvalues
S. C. Reddy and L. N. Trefethen
Comp. Meth. Appl. Mech. Engr. 80 (1990), 147-164.
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82
The CF table
E. Hayashi, L. N. Trefethen and M. H. Gutknecht
Constr. Approx. 6 (1990), 195-223.
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83 A modified Schwarz-Christoffel transformation for elongated regions
L. H. Howell and L. N. Trefethen
SIAM J. Sci. Stat. Comput. 11 (1990), 928-949.
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84 Approximation theory and numerical linear algebra
L. N. Trefethen
In J. C. Mason and M. G. Cox, eds., Algorithms for Approximation II, Chapman and Hall, 1990.
Chapter in book
85 Average-case stability of Gaussian elimination
L. N. Trefethen and R. S. Schreiber
SIAM J. Matrix Anal. Applics. 11 (1990), 335-360.
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86 SCPACK User's Guide
L. N. Trefethen
Numerical Analysis Report 89-2, Dept. of Mathematics, MIT, 1989.
(An earlier edition appeared as an ICASE internal report in 1983.)

87 Schwarz-Christoffel mapping in the 1980's
L. N. Trefethen
Numerical Analysis Report 89-1, Dept. of Mathematics, MIT, 1989.

88 Lax-stability vs. eigenvalue stability of spectral methods
L. N. Trefethen
In K. W. Morton and M. J. Baines, eds., Clarendon Press, 1988.
Chapter in book
89 The eigenvalues of second-order spectral differentiation matrices
J. A. C. Weideman and L. N. Trefethen
SIAM J. Numer. Anal. 25 (1988), 1279-1298.
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90 Ill-posedness of absorbing boundary conditions for migration
L. H. Howell and L. N. Trefethen
Geophysics 53 (1988), 593-603.

91 Fourier analysis of the SOR iteration
R. J. LeVeque and L. N. Trefethen
IMA J. Numer. Anal. 8 (1988), 273-279.
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92
Wide-angle one-way wave equations
L. Halpern and L. N. Trefethen
J. Acoust. Soc. Amer. 84 (1988), 1397-1404.
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93 Padé, stable Padé, and Chebyshev-Padé approximation
L. N. Trefethen and M. H. Gutknecht
In J. Mason, ed., Algorithms for Approximation, Clarendon Press, 1987.
Chapter in book
94 An instability phenomenon in spectral methods
L. N. Trefethen and M. R. Trummer
SIAM J. Numer. Anal. 24 (1987), 1008-1023.
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95 Ideal jet flow in two dimensions
F. Dias, A. R. Elcrat and L. N. Trefethen
J. Fluid Mech. 185 (1987), 275-288.
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96 Numerical Conformal Mapping, editor
L. N. Trefethen
269 pages. Elsevier, 1986.
Book
97 Classical free-streamline flow over a polygonal obstacle
A. R. Elcrat and L. N. Trefethen
J. Comp. Appl. Math. 14 (1986), 251-265.
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98 MATLAB programs for CF approximation
L. N. Trefethen
In C. K. Chui, et al., eds., Approximation Theory V, Academic Press, 1986.
Chapter in book
99 Conformal mapping solution of Laplace's equation on a polygon with oblique derivative boundary conditions
L. N. Trefethen and R. J. Williams
J. Comp. Appl. Math. 14 (1986), 227-249.
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100 Well-posedness of one-way wave equations and absorbing boundary conditions
L. N. Trefethen and L. Halpern
Math. Comp. Vol. 47 No. 176 (1986), 421-435.
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101 Dispersion, dissipation, and stability
L. N. Trefethen
In D. F. Griffiths and G. A. Watson, eds., Numerical Analysis, Longman, 1986.
Chapter in book
102
Three mysteries of Gaussian elimination
L. N. Trefethen
ACM SIGNUM Newsletter, October 1985.
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103 Stability of hyperbolic finite-difference models with one or two boundaries
L. N. Trefethen
In B. E. Engquist, et al., eds., Large-Scale Computations in Fluid Mechanics, v. 2, Amer. Math. Soc., 1985.

104 Stability of finite-difference models containing two boundaries or interfaces
L. N. Trefethen
Math. Comp. Vol. 45 No. 172 (1985), 279-300.
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105 On convergence and degeneracy in rational Padé and Chebyshev approximation
L. N. Trefethen and M. H. Gutknecht
SIAM J. Math. Anal. 16 (1985), 198-210.
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106 Advanced Problems: 6460-6462
L. R. Duffy, L. E. Mattics, R. J. LeVeque and L. N. Trefethen
The American Mathematical Monthly, Vol. 91, No. 6. (Jun. - Jul., 1984), p. 371.
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107 On the resolvent condition in the Kreiss Matrix Theorem
R. J. LeVeque and L. N. Trefethen
BIT 24 (1984), 584-591.
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108 The asymptotic accuracy of rational best approximations to ez on a disk
L. N. Trefethen
J. Approx. Theory 40 (1984), 380-383.
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109 Square blocks and equioscillation in the Padé, Walsh, and CF tables
L. N. Trefethen
In P. R. Graves-Morris, et al., eds., Rational Approximation and Interpolation, Lect. Notes in Math, v. 1105, Springer, 1984.
Chapter in book
110 Real vs. complex rational Chebyshev approximation on complex domains
L. N. Trefethen and M. H. Gutknecht
In L. Collatz et al., eds., Numerical Methods of Approximation Theory, v. 7, Birkhäuser, 1984.
Chapter in book
111 Analysis and design of polygonal resistors by conformal mapping
L. N. Trefethen
Z. Angew. Math. Phys. 35 (1984), 692-704.
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112 Instability of finite difference models for hyperbolic initial boundary value problems
L. N. Trefethen
Comm. Pure Appl. Math. 37 (1984), 329-367.
(This article won the first Fox Prize in Numerical Analysis.)

113 On Lp-instability and dispersion at discontinuities in finite difference schemes
L. N. Trefethen
In R. Vichnevetsky and R. Stepleman, eds., Proc. Fifth IMACS Int. Symp. on Computer Methods for Partial Diffl. Eqs., IMACS, 1984.

114 Fourier Analysis of Numerical Approximations of Hyperbolic Equations, by R. Vichnevetsky and J. B. Bowles
L. N. Trefethen
SIAM Review Vol. 26 No. 3 (1984), 439-441.
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(Book Review)
115 Circularity of the error curve and sharpness of the CF method in complex Chebyshev approximation
L. N. Trefethen
SIAM J. Numer. Anal. 20 (1983), 1258-1263.
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116 The Carathéodory-Fejér (CF) method for recursive digital filter design
M. H. Gutknecht, J. O. Smith and L. N. Trefethen
IEEE Trans. Acoustics, Speech, and Signal Proc. ASSP-31 (1983), 1417-1426.
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117 The Carathéodory-Fejér method for real rational approximation
L. N. Trefethen and M. H. Gutknecht
SIAM J. Numer. Anal. 20 (1983), 420-436.
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118 Real vs. complex rational Chebyshev approximation on an interval
L. N. Trefethen and M. H. Gutknecht
Trans. Amer. Math. Soc. 280 (1983), 555-561.
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119 Nonuniqueness of best rational Chebyshev approximations on the unit disk
M. H. Gutknecht and L. N. Trefethen
J. Approx. Theory 39 (1983), 275-288.
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120 Real and complex Chebyshev approximation on the unit disk and interval
M. H. Gutknecht and L. N. Trefethen
Bull. Amer. Math. Soc. 8 (1983), 455-458.
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121 Chebyshev approximation on the unit disk
L. N. Trefethen
In Computational Aspects of Complex Analysis, H. Werner, et al., eds., D. Reidel, 1983.

122 Group velocity interpretation of the stability theory of Gustafsson, Kreiss, and Sundström
L. N. Trefethen
J. Comp. Phys. 49 (1983), 199-217.
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123 Group velocity in finite difference schemes
L. N. Trefethen
SIAM Review 24 (1982), 113-136.
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124 Real polynomial Chebyshev approximation by the Carathéodory-Fejér method
M. H. Gutknecht and L. N. Trefethen
SIAM J. Numer. Anal. 19 (1982), 358-371.
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125 Rational Chebyshev approximation on the unit disk
L. N. Trefethen
Numer. Math. 37 (1981), 297-320.
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126 Near-circularity of the error curve in complex Chebyshev approximation
L. N. Trefethen
J. Approx. Theory 31 (1981), 344-367.
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127 Computation and application of Schwarz-Christoffel transformations
L. N. Trefethen
In Proceedings of the 1980 Army Numerical Analysis and Computers Conference, Army Research Office.
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(review only)
128 Numerical computation of the Schwarz-Christoffel transformation
L. N. Trefethen
SIAM J. Sci. Stat. Comput. 1 (1980), 82-102.
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PDF (Erratum)