Accelerating convergence of trigonometric approximations

Authors:
William B. Jones and G. Hardy

Journal:
Math. Comp. **24** (1970), 547-560

MSC:
Primary 65.20; Secondary 42.00

DOI:
https://doi.org/10.1090/S0025-5718-1970-0277086-X

MathSciNet review:
0277086

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Abstract: Lanczos has recently developed a method for accelerating the convergence of trigonometric approximations for smooth, nonperiodic functions by modifying their boundary behavior. The method is reformulated here in terms of interpolation theory and is shown to be related to the theory of Lidstone interpolation. Extensions given include a new type of modifying function and the establishment of criteria for the convergence of associated interpolation series. Applications are given for the error function and its derivative.

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Additional Information

DOI:
https://doi.org/10.1090/S0025-5718-1970-0277086-X

Keywords:
Trigonometric approximation,
interpolation series,
accelerating convergence,
Fourier series,
Lidstone interpolation

Article copyright:
© Copyright 1970
American Mathematical Society