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.

### Chebfun fundamentals

- 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

### Books

- Trefethen,
*Approximation Theory and Aproximation Practice*,*SIAM*, 2013 - Trefethen, Birkisson, and Driscoll,
*Exploring ODEs*,*SIAM*, to appear in 2018