Differentiation by integration using orthogonal polynomials, a survey

作者：Diekema Enno; Koornwinder Tom H^*

来源：Journal of Approximation Theory, 2012, 164(5): 637-667.

DOI：10.1016/j.jat.2012.01.003

• Approximated higher order derivative
• Orthogonal polynomial
• Least-square approximation
• Wavelet
• Filter
• Smoothing

This survey paper discusses the history of approximation formulas for n-th order derivatives by integrals involving orthogonal polynomials. There is a large but rather disconnected corpus of literature on such formulas. We give some results in greater generality than in the literature. Notably we unify the continuous and discrete case. We make many side remarks, for instance on wavelets, Mantica%26apos;s Fourier-Bessel functions and Greville%26apos;s minimum R-alpha formulas in connection with discrete smoothing.

• 出版日期2012-5