The Mathematical Institute, University of Oxford, Eprints Archive

An extension of MATLAB to continuous functions and operators

Battels, Zachary and Trefethen, Lloyd N. (2003) An extension of MATLAB to continuous functions and operators. Technical Report. Unspecified. (Submitted)

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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.

Item Type:Technical Report (Technical Report)
Subjects:H - N > Numerical analysis
Research Groups:Numerical Analysis Group
ID Code:1203
Deposited By:Lotti Ekert
Deposited On:18 May 2011 08:11
Last Modified:18 May 2011 08:11

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