Skip to Main Content

Mathematics of Computation

Published by the American Mathematical Society, the Mathematics of Computation (MCOM) is devoted to research articles of the highest quality in all areas of pure and applied mathematics.

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

The 2020 MCQ for Mathematics of Computation is 1.98.

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.

 

The calculation of Fourier coefficients by the Möbius inversion of the Poisson summation formula. II. Piecewise continuous functions and functions with poles near the interval $[0, 1]$
HTML articles powered by AMS MathViewer

by J. N. Lyness PDF
Math. Comp. 25 (1971), 59-78 Request permission

Abstract:

In Part I, the MIPS method for calculating Fourier coefficients was introduced, and applied to functions $f \in {C^{(p)}}[0,1]$. In this part two extensions of the theory are described. One modification extends the theory to piecewise continuous functions, $f \in P{C^{(p)}}[0,1]$. Using these results the method may be used to calculate approximations to trigonometrical integrals (in which the length of the interval need not coincide with a period of the trigonometrical weighting function). The other modification treats functions which are analytic, but whose low-order derivatives vary rapidly due to poles in the complex plane near the interval of integration. Essentially these poles are ’subtracted out’ but this is done implicitly by the inclusion of additional terms in the standard series. The practical application of these modified methods requires that the nature and location of the discontinuities—or poles—be known at least approximately.
References
Similar Articles
  • Retrieve articles in Mathematics of Computation with MSC: 65D30
  • Retrieve articles in all journals with MSC: 65D30
Additional Information
  • © Copyright 1971 American Mathematical Society
  • Journal: Math. Comp. 25 (1971), 59-78
  • MSC: Primary 65D30
  • DOI: https://doi.org/10.1090/S0025-5718-1971-0293846-4
  • MathSciNet review: 0293846