An extension of MATLAB to continuous functions and operators
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 "ch...
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| Veröffentlicht in: | SIAM journal on scientific computing 2004, Vol.25 (5), p.1743-1770 |
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| container_title | SIAM journal on scientific computing |
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| creator | BATTLES, Zachary TREFETHEN, Lloyd N |
| description | 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. |
| doi_str_mv | 10.1137/s1064827503430126 |
| format | Article |
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| issn | 1064-8275 1095-7197 |
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| source | SIAM Journals Online |
| subjects | Approximation Approximations and expansions Exact sciences and technology Fourier transforms Linear algebra Mathematical analysis Mathematics Numerical analysis Numerical analysis. Scientific computation Numerical approximation Sciences and techniques of general use Software Values |
| title | An extension of MATLAB to continuous functions and operators |
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