Numerical Algorithms

, Volume 82, Issue 3, pp 1085–1096 | Cite as

Exponential and trigonometrical fittings: user-friendly expressions for the coefficients

  • L. Gr. IxaruEmail author
Original Paper


The coefficients of numerical methods derived by exponential and trigonometric fittings are functions of parameter z = ωh where ω and h are the involved frequency and the step size, respectively. The problem is that, for the versions described until now in the literature, the accurate computation of each coefficient asks for four different formulas (an analytic formula valid for big z and a power series expansion for small z, in each of the two fittings). In this paper, we describe an algorithm-like technique which allows replacing the set of the four by a single formula. The latter is universally valid, in the sense that it can be successfully applied irrespective of whether z is small or big, or of whether the fitting is trigonometric or exponential. Two sets of special functions, sets C and S, are introduced for this purpose, and their mathematical properties are established. Examples and applications are also presented.


Numerical methods Trigonometric fitting Exponential fitting 


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© Springer Science+Business Media, LLC, part of Springer Nature 2018

Authors and Affiliations

  1. 1.Department of Theoretical Physics“Horia Hulubei” National Institute of Physics and Nuclear EngineeringBucharestRomania
  2. 2.Academy of Romanian ScientistsBucharestRomania

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