Fast algorithms for discrete Chebyshev-Vandermonde transforms and applications
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Applying orthogonal polynomials, the discrete Chebyshev-Vandermonde transform (DCVT) is introduced as a special almost orthogonal transform. An important example of DCVT is the discrete cosine transform (DCT). Using the divide-and-conquer technique and the d'Alembert functional equation, fast DCT-algorithms are described. By the help of these results we present for the first time fast, numerically stable algorithms for simultaneous polynomial approximation and for collocation method for the airfoil equation, a special Cauchytype singular integral equation.
KeywordsIntegral Equation Functional Equation Discrete Cosine Transform Orthogonal Polynomial Fast Algorithm
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