Skip to Main Content

Mathematics of Computation

Published by the American Mathematical Society since 1960 (published as Mathematical Tables and other Aids to Computation 1943-1959), Mathematics of Computation is devoted to research articles of the highest quality in computational mathematics.

ISSN 1088-6842 (online) ISSN 0025-5718 (print)

The 2020 MCQ for Mathematics of Computation is 1.78.

What is MCQ? The Mathematical Citation Quotient (MCQ) measures journal impact by looking at citations over a five-year period. Subscribers to MathSciNet may click through for more detailed information.

 

Accelerating convergence of trigonometric approximations
HTML articles powered by AMS MathViewer

by William B. Jones and G. Hardy PDF
Math. Comp. 24 (1970), 547-560 Request permission

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.
References
  • Milton Abramowitz and Irene A. Stegun, Handbook of mathematical functions with formulas, graphs, and mathematical tables, National Bureau of Standards Applied Mathematics Series, No. 55, U. S. Government Printing Office, Washington, D.C., 1964. For sale by the Superintendent of Documents. MR 0167642
  • Ralph P. Boas Jr. and R. Creighton Buck, Polynomial expansions of analytic functions, Ergebnisse der Mathematik und ihrer Grenzgebiete, (N.F.), Band 19, Academic Press, Inc., Publishers, New York; Springer-Verlag, Berlin, 1964. Second printing, corrected. MR 0162914
  • Philip J. Davis, Interpolation and approximation, Blaisdell Publishing Co. [Ginn and Co.], New York-Toronto-London, 1963. MR 0157156
  • Eugene Isaacson and Herbert Bishop Keller, Analysis of numerical methods, John Wiley & Sons, Inc., New York-London-Sydney, 1966. MR 0201039
  • Dunham Jackson, The theory of approximation, American Mathematical Society Colloquium Publications, vol. 11, American Mathematical Society, Providence, RI, 1994. Reprint of the 1930 original. MR 1451140
  • William B. Jones & G. Hardy, Numerical Prediction of Ionospheric Characteristics, ESSA Technical Report ERL 76-ITS 66, U.S. Government Printing Office, Washington, D.C., 1968. William B. Jones & F. Stewart, Numerical Mapping of Ionospheric Plasma Frequency, paper presented at URSI Spring Meeting in Washington, D.C., 1969.
  • C. Lanczos, Evaluation of noisy data, J. Soc. Indust. Appl. Math. Ser. B Numer. Anal. 1 (1964), 76–85. MR 179909
  • Cornelius Lanczos, Discourse on Fourier series, Hafner Publishing Co., New York, 1966. MR 0199629
  • G. J. Lidstone, "Notes on the extension of Aitken’s theorem (for polynomial interpolation) to the Everett types," Proc. Edinburgh Math. Soc. (2), v. 2, 1929, pp. 16–19. J. M. Whittaker, "On Lidstone series and two-point expansions of analytic functions," Proc. London Math. Soc., v. 36, 1934, pp. 451–469.
  • D. V. Widder, Completely convex functions and Lidstone series, Trans. Amer. Math. Soc. 51 (1942), 387–398. MR 6356, DOI 10.1090/S0002-9947-1942-0006356-4
Similar Articles
  • Retrieve articles in Mathematics of Computation with MSC: 65.20, 42.00
  • Retrieve articles in all journals with MSC: 65.20, 42.00
Additional Information
  • © Copyright 1970 American Mathematical Society
  • 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