| 1 | Numerical Analysis L. N. Trefethen In W. T. Gowers, ed., Princeton Companion to Mathematics, Princeton U. Press. 2008. |
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| 2 |
Computing Aα, log(A), and related matrix functions by contour integrals N. Hale, N. J. Higham and L. N. Trefethen J. Numer. Anal., Vol. 46, No. 5, pp. 2505-2523. 2008. |
3 |
G.H.
Hardy, Applied Mathematician L. N. Trefethen SIAM News, Vol. 41 / No. 3, pp. 1+3, April 2008. |
| 4 |
New Quadrature Formulas from
Conformal Maps N. Hale and L. N. Trefethen J. Numer. Anal., Vol. 46, No. 2, pp. 930-948. 2008. |
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| 5 |
Is Gauss quadrature better than
Clenshaw-Curtis? L. N. Trefethen SIAM Review 50, No. 1, pp. 67-87, 2008. |
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| 6 |
Obituary Gene H. Golub
(1932-2007) L. N. Trefethen Nature, Vol. 450, p. 962, 13 Dec. 2007. |
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| 7 |
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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| 8 |
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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| 9 |
Computing numerically with
functions instead of numbers L. N. Trefethen Math. Comput. Sci. 1 (2007), pp. 9-19. |
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| 10 |
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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| 11 |
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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| 12 |
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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| 13 | 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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| 14 | 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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| 15 | 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 |
| 16 | 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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| 17 | Wave packet pseudomodes of
variable coefficient differential operators L. N. Trefethen Proc. Roy. Soc. Lond. A 561 (2005), 3099-3122. |
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| 18 | Reviving the method of
particular solutions T. Betcke and L. N. Trefethen SIAM Review 47 (2005), 469-491. |
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| 19 | 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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| 20 | 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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| 21 |
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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| 22 | 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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| 23 | Barycentric Lagrange
interpolation J.-P. Berrut and L. N. Trefethen SIAM Review 46 (2004), 501-517. |
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| 24 | 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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| 25 | Linearized pipe flow to
Reynolds number 107 A. Meseguer and L. N. Trefethen J. Comp. Phys. 186 (2003), 178-197. |
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| 26 | 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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| 27 | Schwarz-Christoffel Mapping Tobin A. Driscoll and L. N. Trefethen xvi+132 pages. Cambridge U. Press, 2002. |
Book |
| 28 | Pseudospectra of rectangular
matrices T. G. Wright and L. N. Trefethen IMA J. Numer. Anal. 22 (2002), 501-519. |
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| 29 | 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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| 30 | Chastened Challenge Sponsor: "I
Misjudged" L. N. Trefethen SIAM News, Vol. 35, No. 6, July/Aug. 2002. (follow-up article). |
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| 31 |
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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| 32 | 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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| 33 | 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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| 34 | 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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| 35 | Generalizing eigenvalue
theorems to pseudospectra theorems M. Embree and L. N. Trefethen SIAM J. Sci. Comput. 23 (2001), 583-590. |
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| 36 | Eigenvalues and musical
instruments V. E. Howle and L. N. Trefethen J. Comp. Appl. Math. 135 (2001), 23-40. |
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| 37 | 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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| 38 | Spectral Methods in MATLAB L. N. Trefethen xviii+165 pages. SIAM, 2000. |
Book |
| 39 | Pseudospectra Gateway. M. Embree and L. N. Trefethen Web Site: http://www.comlab.ox.ac.uk/pseudospectra, 2000. |
Web pages |
| 40 | 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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| 41 |
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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| 42 | 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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| 43 | Growth and decay of random
Fibonacci sequences M. Embree and L. N. Trefethen Proc. Royal Soc. Lond. A 455 (1999), 2471-2485. |
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| 44 | 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. |
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| 45 | 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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| 46 | Computation of pseudospectra L. N. Trefethen Acta Numerica 8 (1999), 247-295. |
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| 47 | 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 |
| 48 | 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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| 49 | 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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| 50 | 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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| 51 |
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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| 52 | 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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| 53 | Maxims about numerical
mathematics, computers, science, and life L. N. Trefethen SIAM News v. 31, no. 1 (1998), p. 4. |
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| 54 | 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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| 55 | 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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| 56 | Numerical Linear Algebra L. N. Trefethen and David Bau III xii+361 pages. SIAM, 1997. (SIAM's bestselling book of the past decade.) |
Book |
| 57 | 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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| 58 | 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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| 59 | 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 |
| 60 | 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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| 61 |
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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| 62 | 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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| 63 | 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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| 64 | 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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| 65 | Do the pseudospectra of a
matrix determine its behavior? A. Greenbaum and L. N. Trefethen unpublished technical report, 1995. |
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| 66 | 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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| 67 | 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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| 68 | 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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| 69 | 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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| 70 | 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. |
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| 71 |
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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| 72 | Stiffness of ODEs D. J. Higham and L. N. Trefethen BIT 33 (1993), 285-303. |
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| 73 | 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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| 74 | Pseudospectra of matrices L. N. Trefethen In D. F. Griffiths and G. A. Watson, eds., Numerical Analysis 1991, Longman, 1992. |
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| 75 | Eigenvalues and
pseudo-eigenvalues of Toeplitz matrices L. Reichel and L. N. Trefethen Lin. Alg. Applics. 162-164 (1992), 153-185. |
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| 76 | 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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| 77 | 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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| 78 | Stability of the method of lines S. C. Reddy and L. N. Trefethen Numer. Math. 62 (1992), 235-267. |
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| 79 | 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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| 80 | 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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| 81 |
The CF table E. Hayashi, L. N. Trefethen and M. H. Gutknecht Constr. Approx. 6 (1990), 195-223. |
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| 82 | 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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| 83 | 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 |
| 84 | 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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| 85 | 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.) |
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| 86 | Schwarz-Christoffel mapping in
the 1980's L. N. Trefethen Numerical Analysis Report 89-1, Dept. of Mathematics, MIT, 1989. |
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| 87 | 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 |
| 88 | 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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| 89 | Ill-posedness of absorbing
boundary conditions for migration L. H. Howell and L. N. Trefethen Geophysics 53 (1988), 593-603. |
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| 90 | 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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| 91 |
Wide-angle one-way wave
equations L. Halpern and L. N. Trefethen J. Acoust. Soc. Amer. 84 (1988), 1397-1404. |
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| 92 | 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 |
| 93 | 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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| 94 | 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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| 95 | Numerical Conformal Mapping,
editor L. N. Trefethen 269 pages. Elsevier, 1986. |
Book |
| 96 | 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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| 97 | MATLAB programs for CF
approximation L. N. Trefethen In C. K. Chui, et al., eds., Approximation Theory V, Academic Press, 1986. |
Chapter in book |
| 98 | 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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| 99 | 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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| 100 | Dispersion, dissipation, and
stability L. N. Trefethen In D. F. Griffiths and G. A. Watson, eds., Numerical Analysis, Longman, 1986. |
Chapter in book |
| 101 |
Three mysteries of Gaussian
elimination L. N. Trefethen ACM SIGNUM Newsletter, October 1985. |
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| 102 | 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. |
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| 103 | 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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| 104 | 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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| 105 | 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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| 106 | 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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| 107 | 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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| 108 | 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 |
| 109 | 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 |
| 110 | Analysis and design of
polygonal resistors by conformal mapping L. N. Trefethen Z. Angew. Math. Phys. 35 (1984), 692-704. |
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| 111 | 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.) |
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| 112 | 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. |
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| 113 | 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. |
PDF (Book Review) |
| 114 | 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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| 115 | 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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| 116 | 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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| 117 | 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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| 118 | 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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| 119 | 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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| 120 | Chebyshev approximation on the
unit disk L. N. Trefethen In Computational Aspects of Complex Analysis, H. Werner, et al., eds., D. Reidel, 1983. |
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| 121 | 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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| 122 | Group velocity in finite
difference schemes L. N. Trefethen SIAM Review 24 (1982), 113-136. |
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| 123 | 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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| 124 | Rational Chebyshev
approximation on the unit disk L. N. Trefethen Numer. Math. 37 (1981), 297-320. |
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| 125 | Near-circularity of the error
curve in complex Chebyshev approximation L. N. Trefethen J. Approx. Theory 31 (1981), 344-367. |
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| 126 | Computation and application of
Schwarz-Christoffel transformations L. N. Trefethen In Proceedings of the 1980 Army Numerical Analysis and Computers Conference, Army Research Office. |
PDF (review only) |
| 127 | Numerical computation of the
Schwarz-Christoffel transformation L. N. Trefethen SIAM J. Sci. Stat. Comput. 1 (1980), 82-102. |
PDF PDF (Erratum) |