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Not yet appeared
Numerical computation of the Schwarz function.
Constructive Approximation, submitted.
Unbounded growth of band-limited functions.
Notices of the AMS, submitted.
Evaluation of resonances...,
with Bruno and Santana. SIAM J. Sci. Comput., submitted.
Rational approximation.
Notices of the AMS, to appear.
Computation of Zolotarev rational functions,
with Wilber. SIAM J. Sci. Comput., submitted.
The first five years of the AAA algorithm,
with Nakatsukasa and Sète. Intl. Cong. Basic Sci., to appear.
2024
Sigmoid functions and multiscale resolution of singularities,
with Huybrechs.
SIAM Rev., 66 (2024), 683-693.
Polynomial and rational convergence rates
for Laplace problems on planar domains,
Proc. Roy. Soc. A, 480 (2024), 20240178.
Computation of 2D Stokes flows via lightning and AAA rational approximation,
with Xue and Waters.
SIAM J. Sci. Comput., 46 (2024), A1214-A1234.
AAA rational approximation on a continuum,
with Driscoll and Nakatsukasa.
SIAM J. Sci. Comput., 46 (2024), A929-A952. (Matlab/Julia codes)
2023
Resolution of singularities by rational functions, with Herremans and Huybrechs.
SIAM J. Numer. Anal., 61 (2023), 2580-2600.
Numerical analytic continuation.
Japan J. Indust. Appl. Math., 40 (2023), 1587-1636.
AAA interpolation of equispaced data, with Huybrechs.
BIT Numer. Math., 63 (2023), 21.
Spectacularly large expansion coefficients in Müntz's theorem.
La Matematica, 2 (2023), 31-36.
AAA-least squares rational approximation and
solution of Laplace problems, with Costa.
A. Hujdurović, et al., European Congr. Math., 2023.
2022
An Applied Mathematician's Apology.
SIAM, 2022.
Rectangular eigenvalue problems, with Hashemi and
Nakatsukasa.
Advances in Computational Mathematics, 48:80 (2022).
Exactness of quadrature formulas.
SIAM Rev., 64 (2022), 132-150.
Lightning Stokes solver, with Brubeck.
SIAM J. Sci. Comp., 44 (2022), A1205-A1226.
Numerical Linear Algebra, 25th Anniversary Edition,
with Bau. SIAM, 2022.
2021
Reciprocal-log approximation and planar PDE
solvers,
with Nakatsukasa.
SIAM J. Numer. Anal., 59 (2021), 2801-2822.
Log-lightning computation of capacity and Green's function,
with Baddoo. Maple Trans., 1 (2021), 5:1-5:13.
(video abstract)
Vandermonde with Arnoldi,
with Brubeck and Nakatsukasa.
SIAM Rev., 63 (2021), 405-415.
Exponential node clustering at singularities for rational
approximation, quadrature, and PDEs,
with Nakatsukasa and Weideman.
Numer. Math., 147 (2021), 227-254.
2020
An algorithm for real and complex rational minimax approximation,
with Nakatsukasa. SIAM J. Sci. Comp., 42 (2020), A3157-A3179.
Numerical conformal mapping with rational functions.
Comp. Meth. Funct. Th., 20 (2020), 369-387.
Eight perspectives on an exponentially ill-conditioned ODE.
SIAM Rev., 62 (2020), 439-462.
Quantifying the ill-conditioning of analytic continuation.
BIT Numer. Math., 60 (2020), 901-915.
2019
Approximation Theory and Approximation Practice,
Extended Edition.
SIAM, 2019.
Solving Laplace problems with corner singularities via
rational functions, with Gopal.
SIAM J. Numer. Anal., 57 (2019), 2074-2094.
New Laplace and Helmholtz solvers,
with Gopal.
Proc. Nat. Acad. Sci. USA, 116 (2019), 10223.
Representation of conformal maps by rational functions,
with Gopal. Numer. Math., 142 (2019), 359-382.
Smooth random functions, random ODEs, and Gaussian
processes, with Filip and Javeed.
SIAM Rev., 61 (2019), 185-205.
2018
The AAA algorithm for rational approximation,
with Nakatsukasa and Sète.
SIAM J. Sci. Comp., 40 (2018), A1494-A1522.
Series solution of Laplace problems.
ANZIAM J., 60 (2018), 1-26.
Rational minimax approximation via adaptive
barycentric representations,
with Filip, Nakatsukasa, and Beckermann.
SIAM J. Sci. Comp, 40 (2018), A2427-A2455.
Rational approximation of xn,
with Nakatsukasa.
Proc. Amer. Math. Soc., 146 (2018), 5219-5224.
2017
Exploring ODEs,
with Birkisson and T. Driscoll.
SIAM, 2017.
Block operators and spectral discretizations,
with Aurentz.
SIAM Rev., 59 (2017), 423-446.
Chopping a Chebyshev series,
with Aurentz.
ACM Trans. Math. Softw., 43 (2017), 33.
Trigonometric interpolation and quadrature in perturbed points,
with Austin.
SIAM J. Numer. Anal., 55 (2017), 2113-2122.
Cubature, approximation, and isotropy in the hypercube.
SIAM Rev., 59 (2017), 469-491.
Multivariate polynomial approximation in
the hypercube.
Proc. AMS, 145 (2017), 4837-4844.
Chebfun in three dimensions,
with Hashemi.
SIAM J. Sci. Comp., 39 (2017), C341-C363.
2016
Euler-Maclaurin and Gregory interpolants,
with Javed. Numer. Math. 132 (2016), 201-216.
Inverse Yogiisms.
Notices AMS, 63 (2016).
2015
Computing eigenvalues of real symmetric matrices with rational
filters in real arithmetic, with Austin.
SIAM J. Sci. Comp., 37 (2015), A1365-A1387.
Mathematics of the Faraday Cage,
with Chapman and Hewett.
SIAM Rev., 57 (2015), 398-417.
Extension of Chebfun to periodic functions,
with Wright, Javed, and Montanelli.
SIAM J. Sci. Comp, 37 (2015), C554-C573.
Continuous analogues of matrix factorizations,
with Townsend. Proc. Roy. Soc. A, 471 (2015), 20140585.
Computing numerically with functions instead of numbers.
Comm. ACM, 58 (2015), 91-97.
2014
A trapezoidal rule error bound unifying the
Euler-Maclaurin formula and geometric convergence
for periodic functions, with Javed.
Proc. R. Soc. A, 470 (2014), xx-xx.
Chebfun Guide,
with Driscoll and Hale.
Pafnuty Press, 2014.
The exponentially convergent trapezoidal rule,
with Weideman.
SIAM Rev., 56 (2014), 385-458.
Numerical algorithms based on analytic function
values at roots of unity, with
A. Austin and Kravanja.
SIAM J. Numer. Anal., 52 (2014), 1795-1821.
2013
Gaussian elimination as an iterative algorithm,
with Townsend.
SIAM News, 2013.
An extension of Chebfun to two dimensions,
with Townsend. SIAM J. Sci. Comp., 35 (2013), C495-C518.
Approximation Theory and Approximation
Practice,
SIAM, 2013.
Robust Padé approximation via SVD,
with Gonnet and Güttel.
SIAM Rev., 55 (2013), 101-117.
2012
Chebfun and numerical quadrature,
with Hale.
Sci. China Math., 55 (2012), 1749-1760.
Stability of barycentric interpolation formulas for
extrapolation,
with Webb and Gonnet.
SIAM J. Sci. Comp., 34 (2012), A3009-A3015.
2011
A sinc function analogue of Chebfun,
with Richardson.
SIAM J. Sci. Comp., 33 (2011), 2519-2535.
Robust rational interpolation and least-squares,
with Gonnet and Pachón.
Elect. Trans. Numer. Anal., 38 (2011), 146-167.
Trefethen's Index Cards:
Forty Years of Notes
about People, Words and Mathematics.
World Scientific Publishing, 2011.
Six myths of polynomial interpolation and quadrature.
Maths. Today, 47 (2011), 184-188.
(Persian translation)
A robust implementation of the
Carathéodory-Fejér method for rational approximation,
with Van Deun. BIT Numer. Math., 51 (2011), 1039-1050.
Ten digit problems.
In Schleicher and Lackmann,
eds., Invitation to Mathematics:
From Competitions to Research, Springer, 2011.
Impossibility of fast stable approximation
of analytic functions from equispaced samples,
with Platte and Kuijlaars. SIAM Rev., 53 (2011), 308-318.
2010
Four bugs on a rectangle,
with Chapman and Lottes. Proc. Roy. Soc. A, 467 (2010), 881-896.
Piecewise-smooth chebfuns,
with Pachón and Platte.
IMA J. Numer. Anal., 30 (2010), 898-916.
Householder triangularization of a quasimatrix.
IMA J. Numer. Anal., 30 (2010), 887-897.
Chebfun: A new kind of numerical computing,
with Platte. In Progress in Industrial Mathematics
at ECMI 2008, Springer, 2010.
2009
Barycentric-Remez algorithms for best polynomial
approximation in the chebfun system,
with Pachón. BIT Numer. Anal., 49 (2009), 721-741.
2008
The chebop system for automatic solution of
differential equations,
with Driscoll and Bornemann. BIT Numer. Math., 48 (2008), 701-723.
Numerical analysis.
In Gowers, ed., Princeton Companion to Mathematics,
Princeton U. Press, 2008.
Computing Aα,
log(A), and related matrix functions by contour
integrals,
with Hale and Higham. SIAM J. Numer. Anal., 46 (2008), 2505-2523.
2007
Obituary Gene H. Golub (1932-2007).
Nature, 450 (2007), 962.
Evaluating matrix functions for exponential integrators via
Carathéodory-Fejér
approximation and contour integrals,
with Schmelzer. Elect. Trans. Numer. Anal., 29 (2007), 1-18.
The kink phenomenon in Fejér and
Clenshaw-Curtis quadrature, with
Weideman. Numer. Math., 107 (2007), 707-727.
Computing numerically with functions instead of numbers.
Math. Comput. Sci., 1 (2007), 9-19.
Computing the gamma function using contour
integrals and rational approximations,
with Schmelzer. SIAM J. Numer. Anal., 45 (2007), 558-571.
Parabolic and hyperbolic contours
for computing the Bromwich integral,
with Weideman. Math. Comp., 76 (2007), 1341-1356.
2006
A rational spectral collocation method
with adaptively transformed Chebyshev grid points,
with Tee. SIAM J. Sci. Comp., 28 (2006), No. 5, 1798-1811.
Talbot quadratures and rational approximations
with Weideman and Schmelzer.
BIT Numer. Math., 46 (2006) 46, 653-670.
Computed eigenmodes of planar regions,
with Betcke. In Chernov, et al., eds.,
Recent Advances in Differential Equations
and Mathematical Physics, Contemp. Math. 412,
Amer. Math. Soc., 2006, 297-314.
2005
Spectra and Pseudospectra:
The Behavior of Nonnormal Matrices and
Operators,
with Embree. Princeton U. Press, 2005.
Ten Digit Algorithms.
Numerical Analysis Report 05/13, Oxford University, 2005.
(From the 2005 A. R. Mitchell Lecture, Dundee.)
Wave packet pseudomodes of variable coefficient
differential operators.
Proc. Roy. Soc. Lond. A, 461 (2005), 3099-3122.
Reviving the method of particular solutions,
with Betcke. SIAM Rev., 47 (2005), 469-491.
Fourth-order time-stepping for stiff PDEs, with
Kassam. SIAM J. Sci. Comp., 26 (2005), 1214-1233.
2004
Computations of eigenvalue avoidance in planar domains,
with Betcke. Proc. Appl. Math. Mech., 4 (2004), 634-635.
Wave packet pseudomodes of twisted Toeplitz matrices,
with Chapman. Comm. Pure Appl. Math., 57 (2004), 1233-1264.
An extension of Matlab to continuous functions and operators,
with Battles. SIAM J. Sci. Comp. 25 (2004), 1743-1770.
Barycentric Lagrange interpolation,
with Berrut. SIAM Rev., 46 (2004), 501-517.
2003
An American at Oxford.
Oxford Magazine, May 2003.
(This essay was discussed in the Times Higher Education Supplement and
elsewhere.)
Linearized pipe flow to Reynolds number 107,
with Meseguer. J. Comp. Phys., 186 (2003), 178-197.
A multipole method for Schwarz-Christoffel mapping
of polygons with thousands of sides,
with Banjai. SIAM J. Sci. Comp., 25 (2003), 1042-1065.
2002
Schwarz-Christoffel Mapping, with
Driscoll. Cambridge U. Press, 2002.
Pseudospectra of rectangular matrices,
with Wright. IMA J. Numer. Anal., 22 (2002), 501-519.
Piecewise continuous Toeplitz matrices and operators:
slow approach to infinity,
with Böttcher and Embree.
SIAM J. Matrix Anal. Applics., 24 (2002), 484-489.
A hundred-dollar, hundred-digit challenge.
SIAM News, 35, No. 1, Jan./Feb. 2002.
(This led to two books by Bornemann et al.)
Chastened challenge sponsor: "I misjudged".
SIAM News, 35, No. 6, July/Aug. 2002.
(follow-up article).
2001
Numerical solution of the omitted area
problem of univalent function theory,
with Banjai. Comp. Meth. Func. Th., 1 (2001), 259-273.
Spectra, pseudospectra and localization for random bidiagonal matrices,
with Contedini and Embree.
Comm. Pure Appl. Math., 54 (2001), 595-623.
Large-scale computation of pseudospectra using ARPACK and eigs,
with Wright. SIAM J. Sci. Comput., 23 (2001), 591-605.
Generalizing eigenvalue theorems to pseudospectra theorems,
with Embree. SIAM J. Sci. Comput., 23 (2001), 583-590.
Eigenvalues and musical instruments,
with Howle. J. Comp. Appl. Math., 135 (2001), 23-40.
Computing Lyapunov constants for random recurrences with smooth coefficients,
with Wright. J. Comp. Appl. Math., 132 (2001),
331-340.
2000
Spectral Methods in MATLAB.
SIAM, 2000.
Threshold amplitudes for transition to turbulence in a pipe,
with Chapman, Henningson, Meseguer,
Mullin, and Nieuwstadt.
Num. Anal. Group Report NA 00/17, Oxford U. Computing Lab., 2000.
Predictions for scientific computing fifty years from now.
Mathematics Today, April 2000, 53-57.
(This essay won the Catherine Richards Prize of the Inst. for Maths.
and Applics., 2000.)
How many shuffles to randomize a deck of cards?,
with 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.)
1999
Growth and decay of random Fibonacci sequences,
with Embree. Proc. Roy. Soc. Lond. A, 455 (1999), 2471-2485.
Large-amplitude transient growth in the
linear evolution of equatorial spread F with a sheared zonal flow,
with Flaherty and Seyler. J. Geophys. Res., 104 (1999), 6843.
Spectra and pseudospectra for pipe Poiseuille flow,
with A. E. Trefethen and Schmid.
Comp. Meth. Appl. Mech. Engr., 1926 (1999),
413-420.
Computation of pseudospectra.
Acta Numer., 8 (1999), 247-295.
The Kreiss matrix theorem on a general complex domain,
with Toh.
SIAM J. Matrix Anal. Applics., 21 (1999),
145-165.
Green's functions for multiply connected domains via conformal mapping,
with Embree.
SIAM Rev., 41 (1999), 721-744.
1998
Schwarz-Christoffel mapping in the computer era,
with Driscoll.
Proc. Int. Congr. Math. 1998, 533-542.
From potential theory to matrix iterations in six steps,
with Driscoll and Toh.
SIAM Rev., 40 (1998), 547-578.
Condition numbers of random triangular matrices,
with Viswanath.
SIAM J. Matrix Anal. Applics., 19 (1998), 564-581.
Maxims about numerical mathematics, computers, science, and life.
SIAM News v. 31, no. 1 (1998), p. 4.
The Chebyshev polynomials of a matrix,
with Toh.
SIAM J. Matrix Anal. Applics., 20 (1998), 400-419.
A numerical analyst looks at the 'cutoff phenomenon' in
card shuffling and other Markov chains,
with Jonsson.
In Griffiths, Higham, and
A. Watson, eds., Numerical Analysis 1997, Addison Wesley Longman, 1998.
1997
Numerical Linear Algebra,
with David Bau III.
SIAM, 1997 (SIAM's all-time bestseller.)
Pseudospectra of linear operators.
In ICIAM '95: Proceedings of the Third International Congress on
Industrial and Applied Mathematics, Akademie-Verlag, Berlin, 1996,
pp. 401-434; also SIAM Rev. 39 (1997), 383-406.
Low-dimensional models of subcritical transition to turbulence,
with Baggett. Phys. Fluids, 9 (1997), 1043-1053.
1996
Finite Difference and Spectral Methods for
Ordinary and Partial Differential Equations.
Graduate textbook, unpublished, 1996.
MultiMATLAB: MATLAB on multiple processors, with
A. E. Trefethen, Menon, Chang, Czajkowski, and Myers.
Tech. Rep. CTC96TR293, Cornell Theory Center, 1996.
Matrix behaviour, unitary reducibility, and Hadamard products,
with Viswanath.
Tech. Rep. TR96-1596, Dept. of Comp. Sci., Cornell U., July, 1996.
Pseudospectra for the wave operator with an absorbing boundary,
with Driscoll.
J. Comp. Appl. Math., 69 (1996), 125-142.
Calculation of pseudospectra by the Arnoldi iteration,
with Toh.
SIAM J. Sci. Comp. 17, (1996), 1-15.
1995
A mostly linear model of transition to turbulence,
with Baggett and Driscoll.
Phys. Fluids, 7 (1995), 833-838.
Do the pseudospectra of a matrix determine its behavior?,
with Greenbaum.
Unpublished technical report, 1995.
1994
Pseudospectra of the convection-diffusion operator,
with Reddy. SIAM J. Appl. Math., 54 (1994), 1634-1649.
Pseudozeros of polynomials and pseudospectra of companion matrices,
with Toh.
Numer. Math., 68 (1994), 403-425.
GMRES/CR and Arnoldi/Lanczos as matrix approximation problems,
with Greenbaum.
SIAM J. Sci. Comput., 15 (1994), 359-368.
From the Buffon needle problem to the Kreiss Matrix Theorem,
with Wegert. Amer. Math. Monthly, 101 (1994), 132-139.
1993
Numerical construction of conformal maps.
Appendix to Saff and Snider, Fundamentals of Complex
Analysis, 2nd ed., Prentice Hall, 1993.
Hydrodynamic stability without eigenvalues,
with A. E. Trefethen, Reddy, and T. A. Driscoll.
Science, 261 (1993), 578-584.
Stiffness of ODEs,
with Higham.
BIT Numer. Math., 33 (1993), 285-303.
The definition of numerical analysis.
SIAM News 25, 6 Nov. 1992. Reprinted in Bull. Inst. Maths. and
Applics., 1993 and again as an appendix to Trefethen and
Bau, Numerical Linear Algebra, SIAM, 1997.
1992
Pseudospectra of matrices.
In Griffiths and Watson, eds., Numerical Analysis 1991,
Longman, 1992.
Eigenvalues and pseudo-eigenvalues of Toeplitz matrices,
with Reichel.
Lin. Alg. Applics., 162-164 (1992), 153-185.
How fast are nonsymmetric matrix iterations?,
with Nachtigal and Reddy.
SIAM J. Matrix Anal. Applics., 13 (1992), 778-795.
A hybrid GMRES algorithm for nonsymmetric linear systems,
with Nachtigal and Reichel.
SIAM J. Matrix Anal. Applics., 13 (1992), 796-825.
Stability of the method of lines, with Reddy.
Numer. Math., 62 (1992), 235-267.
1991
Two results on polynomial interpolation in equally spaced points,
with Weideman.
J. Approx. Theory, 65 (1991), 247-260.
1990
Lax-stability of fully discrete spectral methods
via stability regions and pseudo-eigenvalues,
with Reddy.
Comp. Meth. Appl. Mech. Engr., 80 (1990), 147-164.
The CF table,
with Hayashi and Gutknecht.
Constr. Approx., 6 (1990), 195-223.
A modified Schwarz-Christoffel transformation for elongated regions
with Howell.
SIAM J. Sci. Stat. Comput., 11 (1990), 928-949.
Approximation theory and numerical linear algebra.
In Mason and Cox, eds., Algorithms for Approximation II,
Chapman and Hall, 1990.
Average-case stability of Gaussian elimination,
with Schreiber.
SIAM J. Matrix Anal. Applics., 11 (1990), 335-360.
1989
Schwarz-Christoffel mapping in the 1980's.
Numerical Analysis Report 89-1, Dept. of Mathematics, MIT, 1989.
SCPACK User's Guide.
Numerical Analysis Report 89-2, Dept. of Mathematics, MIT, 1989.
(An earlier edition appeared as an ICASE internal report in 1983.)
1988
Lax-stability vs. eigenvalue stability of spectral methods.
In Morton and Baines, eds., Clarendon Press, 1988.
The eigenvalues of second-order spectral differentiation matrices,
with Weideman.
SIAM J. Numer. Anal., 25 (1988), 1279-1298.
Ill-posedness of absorbing boundary conditions for migration,
with Howell.
Geophysics, 53 (1988), 593-603.
Fourier analysis of the SOR iteration,
with LeVeque.
IMA J. Numer. Anal., 8 (1988), 273-279.
Wide-angle one-way wave equations,
with Halpern.
J. Acoust. Soc. Amer., 84 (1988), 1397-1404.
1987
Padé, stable Padé, and Chebyshev-Padé approximation
with Gutknecht. In Mason and Cox, eds.,
Algorithms for Approximation, Clarendon Press, 1987.
An instability phenomenon in spectral methods,
with Trummer.
SIAM J. Numer. Anal., 24 (1987), 1008-1023.
Ideal jet flow in two dimensions,
with Dias and Elcrat.
J. Fluid Mech., 185 (1987), 275-288.
1986
Numerical Conformal Mapping, editor.
Elsevier, 1986.
Classical free-streamline flow over a polygonal obstacle,
with Elcrat.
J. Comp. Appl. Math., 14 (1986), 251-265.
MATLAB programs for CF approximation.
In Chui, et al., eds., Approximation Theory V, Academic Press, 1986.
(This is probably the first research paper ever published containing a MATLAB
program.)
Conformal mapping solution of Laplace's equation
on a polygon with oblique derivative boundary conditions,
with Williams.
J. Comp. Appl. Math., 14 (1986), 227-249.
Well-posedness of one-way wave equations and absorbing boundary conditions,
with Halpern.
Math. Comp., 47 (1986), 421-435.
Dispersion, dissipation, and stability.
In Griffiths and Watson, eds., Numerical Analysis, Longman,
1986.
1985
Three mysteries of Gaussian elimination.
ACM SIGNUM Newsletter, October 1985.
Stability of hyperbolic finite-difference models with one or two boundaries.
In Engquist, et al., eds., Large-Scale Computations in Fluid
Mechanics, v. 2, Amer. Math. Soc., 1985.
Stability of finite-difference models
containing two boundaries or interfaces.
Math. Comp., 45 (1985), 279-300.
On convergence and degeneracy in rational
Padé and Chebyshev approximation,
with Gutknecht.
SIAM J. Math. Anal., 16 (1985), 198-210.
1984
On the resolvent condition in the Kreiss Matrix Theorem,
with LeVeque.
BIT Numer. Math., 24 (1984), 584-591.
The asymptotic accuracy of rational best
approximations to ez on a disk.
J. Approx. Th., 40 (1984), 380-383.
Square blocks and equioscillation in the
Padé, Walsh, and CF tables.
In Graves-Morris, et al., eds., Rational Approximation and
Interpolation, Lect. Notes in Math, v. 1105, Springer, 1984.
Real vs. complex rational Chebyshev approximation on complex domains,
with Gutknecht.
In Collatz et al., eds., Numerical Methods of Approximation Theory,
v. 7, Birkhäuser, 1984.
Analysis and design of polygonal resistors by conformal mapping,
Z. Angew. Math. Phys., 35 (1984), 692-704.
Instability of finite difference models
for hyperbolic initial boundary value problems.
Comm. Pure Appl. Math., 37 (1984), 329-367.
(This article won the first Fox Prize in Numerical Analysis.)
On Lp-instability and oscillation at
discontinuities in finite difference schemes.
In Vichnevetsky and Stepleman, eds., Proc. Fifth IMACS Int. Symp.
on Computer Methods for Partial Diffl. Eqs., IMACS, 1984.
Fourier Analysis of Numerical Approximations of
Hyperbolic Equations, by Vichnevetsky and
Bowles, SIAM Rev., 26 (1984), 439-441
(book review).
1983
Circularity of the error curve and sharpness
of the CF method in complex Chebyshev approximation.
SIAM J. Numer. Anal., 20 (1983), 1258-1263.
The Carathéodory-Fejér (CF) method for recursive digital
filter design, with
Gutknecht and Smith.
IEEE Trans. Acoust., Speech, Sign. Proc. ASSP-31 (1983),
1417-1426.
The Carathéodory-Fejér method
for real rational approximation,
with Gutknecht.
SIAM J. Numer. Anal. 20 (1983), 420-436.
Real vs. complex rational Chebyshev approximation on an interval,
with Gutknecht.
Trans. Amer. Math. Soc., (1983), 555-561.
Nonuniqueness of best rational Chebyshev approximations on the unit disk,
with Gutknecht.
J. Approx. Th., 39 (1983), 275-288.
Real and complex Chebyshev approximation on the unit disk and interval,
with Gutknecht.
Bull. Amer. Math. Soc., 8 (1983), 455-458.
Chebyshev approximation on the unit disk.
In Computational Aspects of Complex Analysis, Werner, et al., eds.,
D. Reidel, 1983.
Group velocity interpretation of the stability
theory of Gustafsson, Kreiss, and Sundström.
J. Comp. Phys., 49 (1983), 199-217.
1982
Group velocity in finite difference schemes.
SIAM Rev., 24 (1982), 113-136.
Real polynomial Chebyshev approximation by
the Carathéodory-Fejér method,
with Gutknecht.
SIAM J. Numer. Anal., 19 (1982), 358-371.
1981
Rational Chebyshev approximation on the unit disk.
Numer. Math., 37 (1981), 297-320.
Near-circularity of the error curve in complex Chebyshev approximation.
J. Approx. Theory, 31 (1981), 344-367.
Numerical Analysis Program Library User's Guide,
SLAC, Stanford, 1981.
1980
Computation and application of Schwarz-Christoffel transformations.
In Proceedings of the 1980 Army Numerical Analysis and
Computers Conference, Army Research Office.
Numerical computation of the Schwarz-Christoffel transformation
and
erratum.
SIAM J. Sci. Stat. Comput., 1 (1980), 82-102.
1977
Chebyshev Approximation by Polynomials in the Complex Plane, undergraduate
thesis at Harvard College.