On the Chebyshev approximation of a function with two variables
arXiv:1504.046931.26 citations
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This provides a theoretical foundation for multivariate Chebyshev approximation, but the contribution is incremental as it extends known techniques to two variables.
The paper presents a method using the two-dimensional discrete Fourier transform to construct a Chebyshev polynomial approximation for functions of two variables, with a proof of uniform convergence.
There is presented an approach to find an approximation polynomial of a function with two variables based on the two dimensional discrete Fourier transform. The approximation polynomial is expressed through Chebyshev polynomials. There is given an uniform convergence result.