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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.

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Frequency fitting of rational approximations to the exponential functions
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by A. Iserles and S. P. Nørsett PDF
Math. Comp. 40 (1983), 547-559 Request permission


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.
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Additional Information
  • © Copyright 1983 American Mathematical Society
  • Journal: Math. Comp. 40 (1983), 547-559
  • MSC: Primary 41A20; Secondary 65L05
  • DOI:
  • MathSciNet review: 689470