To cite Chebfun in a publication, we recommend the following:
T. A. Driscoll, N. Hale, and L. N. Trefethen, editors, Chebfun Guide, Pafnuty Publications, Oxford, 2014.
Below is a list of some of the Chebfun-related papers written by members of the Chebfun Team. For convenience, a (partially complete) BibTeX file is available. There are also many Chebfun-related publications by others. If you use Chebfun in a book, paper, website, or other project, we'd love to hear about it.
- Battles and Trefethen, An extension of Matlab to continuous functions and operators, SIAM J. Sci. Comp. 2004
- Pachón, Platte and Trefethen, Piecewise smooth chebfuns, IMA J. Numer. Anal. 2010
- Platte and Trefethen, Chebfun: a new kind of numerical computing, ECMI 2008 Proceedings 2010
- Wright, Javed, Montanelli and Trefethen, Extension of Chebfun to periodic functions, SIAM J. Sci. Comp. 2015
- Trefethen, Computing numerically with functions instead of numbers, Commun. of the ACM 2015
- Aurentz and Trefethen, Chopping a Chebyshev series, Trans. Math. Softw., 2017
ODEs, PDEs, integral equations
- Driscoll, Bornemann and Trefethen, The chebop system for automatic solution of differential equations, BIT Numer. Math. 2008
- Driscoll, Automatic spectral collocation for integral, integro-differential, and integrally reformulated differential equations, J. Comp. Phys. 2010
- Webb, Computing complex singularities of differential equations with Chebfun, SIAM Undergrad. Res. Online 2011
- Birkisson and Driscoll, Frechet diﬀerentiation for the numerical solution of boundary-value problems, ACM Trans. Math. Softw. 2012
- Xu and Hale, Explicit construction of rectangular differentiation matrices, IMA J. of Numer. Anal. 2015
- Driscoll and Hale, Rectangular spectral collocation, IMA J. of Numer. Anal. 2016
- Montanelli and Gushterov, Computing planar and spherical choreographies, SIAM J. Appl. Dyn. Syst. 2016
- Aurentz and Trefethen, Block operators and spectral discretizations, see under "Links with linear algebra"
- Montanelli, Computing hyperbolic choreographies, Regul. Chaotic. Dyn. 2016
- Montanelli and Bootland, Solving periodic semilinear stiff PDEs in 1D, 2D and 3D with exponential integrators, submitted
- Montanelli and Nakatsukasa, Fourth-order time-stepping for stiff PDEs on the sphere, to appear in SIAM J. Sci. Comp.
- Birkisson, Automatic reformulation of ODEs to systems of first order equations, submitted.
- Trefethen, Birkisson, and Driscoll, Exploring ODEs, see under "Books"
Chebfun in 2D and 3D
- Townsend and Trefethen, An extension of Chebfun to two dimensions SIAM J. Sci. Comp. 2013
- Nakatsukasa, Noferini, and Townsend, Computing the common zeros of two bivariate functions via Bezout resultants, Numer. Math. 2014
- Townsend, Wilber and Wright, Computing with functions in spherical and polar geometries I. The sphere, SIAM J. Sci. Comp. 2016
- Townsend, Wilber and Wright, Computing with functions in spherical and polar geometries II. The disk, SIAM J. Sci. Comp., in revision
- Hashemi and Trefethen, Chebfun in three dimensions, SIAM J. Sci. Comp., 2017
- Montanelli and Nakatsukasa, Fourth-order time-stepping for stiff PDEs on the sphere, see under "ODEs, PDEs, integral equations"
Links with linear algebra
- Trefethen, Householder triangularization of a quasimatrix, IMA J. Numer. Anal. 2010
- Townsend and Trefethen, Gaussian elimination as an iterative algorithm, SIAM News 2013
- Townsend and Trefethen, Continuous analogues of matrix factorizations, Proc. Royal Soc. A 2015
- Aurentz and Trefethen, Block operators and spectral discretizations, SIAM Rev. 2017
- Hashemi and Nakatsukasa, On the spectral problem for trivariate functions, submitted
Approximation theory and practice
- Pachón and Trefethen, Barycentric- Remez algorithms for best polynomial approximation in the chebfun system, BIT Numer. Math. 2009
- Richardson and Trefethen, A sinc function analogue of Chebfun, SIAM J. Sci. Comp. 2011
- Trefethen, Six myths of polynomial interpolation and quadrature, Maths. Today 2011
- Van Deun and Trefethen, A robust implementation of the Carathéodory-Fejér method, BIT Numer. Math. 2011
- Platte, Trefethen and Kuijlaars, Impossibility of fast stable approximation of analytic functions from equispaced samples, SIAM Rev. 2011
- Gonnet, Pachón and Trefethen, Robust rational interpolation and least-squares, Electr. Trans. Numer. Anal. 2013
- Webb, Trefethen and Gonnet, Stability of barycentric interpolation formulas for extrapolation, SIAM J. Sci. Comp. 2012
- Gonnet, Güttel and Trefethen, Robust Padé approximation via SVD, SIAM Rev. 2013
- Trefethen, Approximation Theory and Approximation Practice, see under "Books"
- Austin, Kravanja and Trefethen, Numerical algorithms based on analytic function values at roots of unity, SIAM J. Numer. Anal. 2014
- Driscoll and Weideman, Optimal domain splitting for interpolation by Chebyshev polynomials, SIAM J. Numer. Anal. 2014
- Xu, The Chebyshev points of the first kind, Appl. Numer. Math. 2016
- Austin and Xu, On the numerical stability of the second barycentric formula for trigonometric interpolation in shifted equispaced points, IMA J. Numer. Anal. 2016
- Trefethen, Cubature, approximation, and isotropy in the hypercube, SIAM Rev. 2017
- Nakatsukasa, Sète and Trefethen, The AAA algorithm for rational approximation, SIAM J. Sci. Comp., submitted
- Trefethen, Multivariate polynomial approximation in the hypercube, Proc. AMS, 2017
- Filip, Nakatsukasa, Trefethen and Beckermann, Rational minimax approximation via adaptive barycentric representations, SIAM J. Sci. Comp., submitted
Orthogonal polynomials and quadrature
- Hale and Trefethen, Chebfun and numerical quadrature, Science in China 2012
- Hale and Townsend, Fast and accurate computation of Gauss–Legendre and Gauss–Jacobi quadrature nodes and weights, SIAM J. Sci. Comp. 2013
- Hale and Townsend, An algorithm for the convolution of Legendre series, SIAM J. Sci. Comp. 2014
- Hale and Townsend, A fast, simple, and stable Chebyshev–Legendre transform using an asymptotic formula, SIAM J. Sci. Comp. 2014
- Hale and Townsend, A fast FFT-based discrete Legendre transform, IMA J. Numer. Anal. 2015
One- and two-page summaries
- Trefethen, Chebfun and Chebop, IMAJNA Newsletter, 2008
- Trefethen, Approximation theory and practice, Oxford Maths. Inst. Newsletter, 2009
- Trefethen, Two-page summary of the main features of Chebfun, 2014
- Trefethen, Approximation Theory and Aproximation Practice, SIAM, 2013
- Trefethen, Birkisson, and Driscoll, Exploring ODEs, SIAM, to appear in 2018