Chebfun is a collection of algorithms and a software system in object-oriented MATLAB that extends familiar powerful methods of numerical computation involving numbers to continuous or piecewise-continuous functions. It also implements continuous analogues of linear algebra notions like the QR decomposition and the SVD, and solves ordinary differential equations. The mathematical basis of the system combines tools of Chebyshev expansions, fast Fourier transform, barycentric interpolation, recursive zerofinding, and automatic differentiation. (Source:

References in zbMATH (referenced in 157 articles , 1 standard article )

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  1. Adcock, Ben; Martín-Vaquero, Jesús; Richardson, Mark: Resolution-optimal exponential and double-exponential transform methods for functions with endpoint singularities (2017)
  2. Georgieva, I.; Hofreither, C.: An algorithm for low-rank approximation of bivariate functions using splines (2017)
  3. Kao, Chiu-Yen; Lai, Rongjie; Osting, Braxton: Maximization of Laplace-Beltrami eigenvalues on closed Riemannian surfaces (2017)
  4. Nakatsukasa, Yuji; Noferini, Vanni; Townsend, Alex: Vector spaces of linearizations for matrix polynomials: a bivariate polynomial approach (2017)
  5. Noferini, Vanni; Pérez, Javier: Chebyshev rootfinding via computing eigenvalues of colleague matrices: when is it stable? (2017)
  6. Area, Iván; Dimitrov, Dimitar K.; Godoy, Eduardo; Paschoa, Vanessa G.: Approximate calculation of sums. II: Gaussian type quadrature (2016)
  7. Bornemann, Folkmar: The SIAM 100-Digit Challenge: a decade later. Inspirations, ramifications, and other eddies left in its wake (2016)
  8. Chadha, Naresh M.; Madden, Niall: An optimal time-stepping algorithm for unsteady advection-diffusion problems (2016)
  9. Costabile, F.; Napoli, A.: A new spectral method for a class of linear boundary value problems (2016)
  10. de la Hoz, Francisco; Cuesta, Carlota M.: A pseudo-spectral method for a non-local KdV-Burgers equation posed on $\mathbbR$ (2016)
  11. Driscoll, Tobin A.; Hale, Nicholas: Rectangular spectral collocation (2016)
  12. Du, Kui: On well-conditioned spectral collocation and spectral methods by the integral reformulation (2016)
  13. Dumitrescu, Bogdan; Şicleru, Bogdan C.; Avram, Florin: Modeling probability densities with sums of exponentials via polynomial approximation (2016)
  14. Greenbaum, Anne; Caldwell, Trevor; Li, Kenan: Near normal dilations of nonnormal matrices and linear operators (2016)
  15. Harrison, Robert J.; Beylkin, Gregory; Bischoff, Florian A.; Calvin, Justus A.; Fann, George I.; Fosso-Tande, Jacob; Galindo, Diego; Hammond, Jeff R.; Hartman-Baker, Rebecca; Hill, Judith C.; Jia, Jun; Kottmann, Jakob S.; Yvonne Ou, M.-J.; Pei, Junchen; Ratcliff, Laura E.; Reuter, Matthew G.; Richie-Halford, Adam C.; Romero, Nichols A.; Sekino, Hideo; Shelton, William A.; Sundahl, Bryan E.; Thornton, W.Scott; Valeev, Edward F.; Vázquez-Mayagoitia, Álvaro; Vence, Nicholas; Yanai, Takeshi; Yokoi, Yukina: MADNESS: a multiresolution, adaptive numerical environment for scientific simulation (2016)
  16. Hosseini, Bamdad; Nigam, Nilima; Stockie, John M.: On regularizations of the Dirac delta distribution (2016)
  17. Hosseini, S.A.; Abdi, A.: On the numerical stability of the linear barycentric rational quadrature method for Volterra integral equations (2016)
  18. Kazashi, Yoshihito: A fully discretised polynomial approximation on spherical shells (2016)
  19. Lubinsky, Doron S.; Pritsker, Igor E.; Xie, X.: Expected number of real zeros for random linear combinations of orthogonal polynomials (2016)
  20. März, Thomas; Rockstroh, Parousia; Ruuth, Steven J.: An embedding technique for the solution of reaction-diffusion equations on algebraic surfaces with isolated singularities (2016)

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