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 174 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. Aurentz, Jared L.; Trefethen, Lloyd N.: Block operators and spectral discretizations (2017)
  3. Bos, L.; De Marchi, S.; Vianello, M.: Polynomial approximation on Lissajous curves in the $d$-cube (2017)
  4. Chapman, S.J.; Farrell, Patrick E.: Analysis of Carrier’s problem (2017)
  5. Choi, Sou-Cheng T.; Ding, Yuhan; Hickernell, Fred J.; Tong, Xin: Local adaption for approximation and minimization of univariate functions (2017)
  6. Figueras, Jordi-Lluís; Gameiro, Marcio; Lessard, Jean-Philippe; de la Llave, Rafael: A framework for the numerical computation and a posteriori verification of invariant objects of evolution equations (2017)
  7. Georgieva, I.; Hofreither, C.: An algorithm for low-rank approximation of bivariate functions using splines (2017)
  8. Gera, P.; Salac, D.: Cahn-Hilliard on surfaces: a numerical study (2017)
  9. Hashemi, Behnam; Trefethen, Lloyd N.: Chebfun in three dimensions (2017)
  10. Kao, Chiu-Yen; Lai, Rongjie; Osting, Braxton: Maximization of Laplace-Beltrami eigenvalues on closed Riemannian surfaces (2017)
  11. Lawrence, Piers W.; Pérez, Javier: Constructing strong linearizations of matrix polynomials expressed in Chebyshev bases (2017)
  12. Nakatsukasa, Yuji; Noferini, Vanni; Townsend, Alex: Vector spaces of linearizations for matrix polynomials: a bivariate polynomial approach (2017)
  13. Napoli, Anna; Abd-Elhameed, W.M.: An innovative harmonic numbers operational matrix method for solving initial value problems (2017)
  14. Noferini, Vanni; Pérez, Javier: Chebyshev rootfinding via computing eigenvalues of colleague matrices: when is it stable? (2017)
  15. Russell, Stephen; Madden, Niall: An introduction to the analysis and implementation of sparse grid finite element methods (2017)
  16. Trefethen, Lloyd N.: Cubature, approximation, and isotropy in the hypercube (2017)
  17. Trefethen, Lloyd N.: Multivariate polynomial approximation in the hypercube (2017)
  18. Wilber, Heather; Townsend, Alex; Wright, Grady B.: Computing with functions in spherical and polar geometries. II: The disk (2017)
  19. Area, Iván; Dimitrov, Dimitar K.; Godoy, Eduardo; Paschoa, Vanessa G.: Approximate calculation of sums. II: Gaussian type quadrature (2016)
  20. Bornemann, Folkmar: The SIAM 100-Digit Challenge: a decade later. Inspirations, ramifications, and other eddies left in its wake (2016)

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