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.

 

Frequency fitting of rational approximations to the exponential functions
HTML articles powered by AMS MathViewer

by A. Iserles and S. P. Nørsett PDF
Math. Comp. 40 (1983), 547-559 Request permission

Abstract:

Rational approximations to the exponential function are considered. Let $R = P/Q$, $\deg P = \deg Q = n$, $R(z) = \exp (z) + \mathcal {O}({z^{2n - 1}})$ and $R( \pm iT) = \exp ( \pm iT)$ for a given positive number T. We show that this approximation is A-acceptable if and only if T belongs to one of intervals, whose endpoints are related to zeros of certain Bessel functions. The existence of this type of approximation and its connection to diagonal Padé approximations is studied. Approximations which interpolate the exponential on the imaginary axis are important in the numerical analysis of highly-oscillatory ordinary differential systems.
References
Similar Articles
  • Retrieve articles in Mathematics of Computation with MSC: 41A20, 65L05
  • Retrieve articles in all journals with MSC: 41A20, 65L05
Additional Information
  • © Copyright 1983 American Mathematical Society
  • Journal: Math. Comp. 40 (1983), 547-559
  • MSC: Primary 41A20; Secondary 65L05
  • DOI: https://doi.org/10.1090/S0025-5718-1983-0689470-X
  • MathSciNet review: 689470