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 304 articles , 2 standard articles )

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  1. Askham, Travis; Rachh, Manas: A boundary integral equation approach to computing eigenvalues of the Stokes operator (2020)
  2. Berrut, Jean-Paul; Elefante, Giacomo: A periodic map for linear barycentric rational trigonometric interpolation (2020)
  3. Breden, Maxime; Kuehn, Christian: Computing invariant sets of random differential equations using polynomial chaos (2020)
  4. Crespo, S.; Fasondini, M.; Klein, C.; Stoilov, N.; Vallée, C.: Multidomain spectral method for the Gauss hypergeometric function (2020)
  5. Elgindy, Kareem T.; Refat, Hareth M.: High-order Gegenbauer integral spectral element method integrated with an adaptive Chebyshev optimization strategy for solving linear singularly perturbed differential equations (2020)
  6. Horning, Andrew; Townsend, Alex: FEAST for differential eigenvalue problems (2020)
  7. Magherini, Cecilia: A corrected spectral method for Sturm-Liouville problems with unbounded potential at one endpoint (2020)
  8. Matharu, Pritpal; Protas, Bartosz: Optimal closures in a simple model for turbulent flows (2020)
  9. Nakatsukasa, Yuji: Sharp error bounds for Ritz vectors and approximate singular vectors (2020)
  10. Opmeer, Mark R.: Decay of singular values for infinite-dimensional systems with Gevrey regularity (2020)
  11. Pan, Jiajia; Li, Huiyuan: A new collocation method using near-minimal Chebyshev quadrature nodes on a square (2020)
  12. Trefethen, Lloyd N.: Approximation theory and approximation practice (2020)
  13. Aiton, Kevin W.; Driscoll, Tobin A.: An adaptive partition of unity method for multivariate Chebyshev polynomial approximations (2019)
  14. Aurentz, Jared L.; Austin, Anthony P.; Benzi, Michele; Kalantzis, Vassilis: Stable computation of generalized matrix functions via polynomial interpolation (2019)
  15. Brugnano, Luigi; Gurioli, Gianmarco; Sun, Yajuan: Energy-conserving Hamiltonian boundary value methods for the numerical solution of the Korteweg-de Vries equation (2019)
  16. Demanet, Laurent; Townsend, Alex: Stable extrapolation of analytic functions (2019)
  17. DeVore, Ronald; Foucart, Simon; Petrova, Guergana; Wojtaszczyk, Przemyslaw: Computing a quantity of interest from observational data (2019)
  18. Filip, Silviu; Javeed, Aurya; Trefethen, Lloyd N.: Smooth random functions, random ODEs, and Gaussian processes (2019)
  19. Foucart, Simon; Lasserre, Jean Bernard: Computation of Chebyshev polynomials for union of intervals (2019)
  20. Gilles, Marc Aurèle; Townsend, Alex: Continuous analogues of Krylov subspace methods for differential operators (2019)

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