An Extension of MATLAB to Continuous Functions and Operators

Authors:
Zachary Battles;Lloyd N. Trefethen
Affiliations:
-;-
Venue:
SIAM Journal on Scientific Computing
Year:
2004

Citing 0
Cited 19

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Numerical experiments on the accuracy of the Chebyshev-Frobenius companion matrix method for finding the zeros of a truncated series of Chebyshev polynomials

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Computing the zeros of a Fourier series or a Chebyshev series or general orthogonal polynomial series with parity symmetries

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Hyperinterpolation in the cube

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Bivariate Lagrange interpolation at the Padua points: Computational aspects

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A fast numerical solution method for two dimensional Fredholm integral equations of the second kind

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On the uniform convergence of the Chebyshev interpolants for solitons

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Automatic spectral collocation for integral, integro-differential, and integrally reformulated differential equations

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Computing near-best fixed pole rational interpolants

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An Improved Arc Algorithm for Detecting Definite Hermitian Pairs

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New series for the cosine lemniscate function and the polynomialization of the lemniscate integral

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Sturm root counting using chebyshev expansion

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Barycentric rational interpolation with asymptotically monitored poles

Numerical Algorithms
A Krylov Method for the Delay Eigenvalue Problem

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A Sinc Function Analogue of Chebfun

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A review of error estimation in adaptive quadrature

ACM Computing Surveys (CSUR)
Analysis of cutoff wavelength of elliptical waveguide by regularized meshless method

International Journal of Numerical Modelling: Electronic Networks, Devices and Fields
Swarm interpolation using an approximate chebyshev distribution

ANTS'12 Proceedings of the 8th international conference on Swarm Intelligence
Recent advances in linear barycentric rational interpolation

Journal of Computational and Applied Mathematics

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Abstract

An object-oriented MATLAB system is described for performing numerical linear algebra on continuous functions and operators rather than the usual discrete vectors and matrices. About eighty MATLAB functions from plot and sum to svd and cond have been overloaded so that one can work with our "chebfun" objects using almost exactly the usual MATLAB syntax. All functions live on [-1,1] and are represented by values at sufficiently many Chebyshev points for the polynomial interpolant to be accurate to close to machine precision. Each of our overloaded operations raises questions about the proper generalization of familiar notions to the continuous context and about appropriate methods of interpolation, differentiation, integration, zerofinding, or transforms. Applications in approximation theory and numerical analysis are explored, and possible extensions for more substantial problems of scientific computing are mentioned.