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 412 articles , 2 standard articles )

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  1. Abdi, A.; Berrut, J.-P.; Hosseini, S. A.: Explicit methods based on barycentric rational interpolants for solving non-stiff Volterra integral equations (2022)
  2. Boito, Paola; Eidelman, Yuli; Gemignani, Luca: Computing the reciprocal of a (\phi)-function by rational approximation (2022)
  3. Hanke, Michael; März, Roswitha: Towards a reliable implementation of least-squares collocation for higher index differential-algebraic equations. I: Basics and ansatz function choices (2022)
  4. Jaquette, Jonathan; Lessard, Jean-Philippe; Takayasu, Akitoshi: Global dynamics in nonconservative nonlinear Schrödinger equations (2022)
  5. Jiang, Haiyan; Lu, Tiao; Zhang, Weitong: A hybrid sinc-Galerkin/finite-difference method for the time-dependent Wigner equation (2022)
  6. Knox, Thomas A.: Approximation of sign-regular kernels (2022)
  7. Mattey, Revanth; Ghosh, Susanta: A novel sequential method to train physics informed neural networks for Allen Cahn and Cahn Hilliard equations (2022)
  8. North, Evan; Tsynkov, Semyon; Turkel, Eli: Non-iterative domain decomposition for the Helmholtz equation with strong material discontinuities (2022)
  9. Overton, Michael L.: Local minimizers of the Crouzeix ratio: a nonsmooth optimization case study (2022)
  10. Trefethen, Lloyd N.: Exactness of quadrature formulas (2022)
  11. An, Congpei; Wu, Hao-Ning: Tikhonov regularization for polynomial approximation problems in Gauss quadrature points (2021)
  12. Aslani, Kyriaki-Evangelia; Sarris, Ioannis E.: Effect of micromagnetorotation on magnetohydrodynamic Poiseuille micropolar flow: analytical solutions and stability analysis (2021)
  13. Bai, Yuexing; Chaolu, Temuer; Bilige, Sudao: Physics informed by deep learning: numerical solutions of modified Korteweg-de Vries equation (2021)
  14. Benner, Peter; Köhler, Martin; Saak, Jens: Matrix equations, sparse solvers: \textttM-M.E.S.S.-2.0.1 -- philosophy, features, and application for (parametric) model order reduction (2021)
  15. Berberich, Jonas P.; Chandrashekar, Praveen; Klingenberg, Christian: High order well-balanced finite volume methods for multi-dimensional systems of hyperbolic balance laws (2021)
  16. Bremer, James; Pang, Qiyuan; Yang, Haizhao: Fast algorithms for the multi-dimensional Jacobi polynomial transform (2021)
  17. Brimacombe, Chris; Corless, Robert M.; Zamir, Mair: Computation and applications of Mathieu functions: a historical perspective (2021)
  18. Casulli, Angelo; Robol, Leonardo: Rank-structured QR for Chebyshev rootfinding (2021)
  19. Celora, Giulia L.; Byrne, Helen M.; Zois, Christos E.; Kevrekidis, P. G.: Phenotypic variation modulates the growth dynamics and response to radiotherapy of solid tumours under normoxia and hypoxia (2021)
  20. Chen, Hongjia; Xu, Kuan: On the backward error incurred by the compact rational Krylov linearization (2021)

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