A Proof, Based on the Euler Sum Acceleration, of the Recovery of an Exponential (Geometric) Rate of Convergence for the Fourier Series of a Function with Gibbs Phenomenon

Author:

Boyd John P.

Publisher

Springer Berlin Heidelberg

Reference16 articles.

1. Boyd, J.P.: A lag-averaged generalization of Euler’s method for accelerating series. Appl. Math. Comput. 72, 146–166 (1995)

2. Boyd, J.P.: The Erfc-Log filter and the asymptotics of the Vandeven and Euler sequence accelerations. In: A.V. Ilin, L.R. Scott (eds.) Proceedings of the 3rd International Conference on Spectral and High Order Methods, pp. 267–276. Houston J. Mathematics, Houston (1996)

3. Boyd, J.P.: Trouble with Gegenbauer reconstruction for defeating Gibbs’ phenomenon: Runge phenomenon in the diagonal limit of Gegenbauer polynomial approximations. J. Comput. Phys. 204(1), 253–264 (2005)

4. Boyd, J.P.: Exponentially accurate Runge-free approximation of non-periodic functions from samples on an evenly-spaced grid. Appl. Math. Lett. 20(9), 971–975 (2007)

5. Boyd, J.P.: Acceleration of algebraically-converging Fourier series when the coefficients have series in powers of 1∕n. J. Comput. Phys. 228(5), 1401–1411 (2008)

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