publication . Preprint . 2018

Fast Switch and Spline Scheme for Accurate Inversion of Nonlinear Functions: The New First Choice Solution to Kepler's Equation

Tommasini, Daniele; Olivieri, David N.;
Open Access English
  • Published: 05 Dec 2018
Abstract
Numerically obtaining the inverse of a function is a common task for many scientific problems, often solved using a Newton iteration method. Here we describe an alternative scheme, based on switching variables followed by spline interpolation, which can be applied to monotonic functions under very general conditions. To optimize the algorithm, we designed a specific ultra-fast spline routine. We also derive analytically the theoretical errors of the method and test it on examples that are of interest in physics. In particular, we compute the real branch of Lambert's $W(y)$ function, which is defined as the inverse of $x \exp(x)$, and we solve Kepler's equation. ...
Subjects
free text keywords: Physics - Computational Physics, Astrophysics - Earth and Planetary Astrophysics, Physics - Space Physics
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