Nonlinear function inversion using k-vector

David Arnas and Daniele Mortari

Applied Mathematics and Computation, 2018, vol. 320, issue C, 754-768

Abstract: This work introduces a general numerical technique to invert one dimensional analytic or tabulated nonlinear functions in assigned ranges of interest. The proposed approach is based on an “optimal” version of the k-vector range searching, an ad-hoc modification devised for function inversion. The optimality consists of retrieving always the same number of data (1,2,⋯) for a specified searching range to initiate the root solver. This provides flexibility to adapt the technique to a variety of root solvers (e.g., bisection, Newton, etc.), using a specified number of starting points. The proposed method allows to build an inverse function toolbox for a set of specified nonlinear functions. In particular, the method is suitable when intensive inversions of the same function are required. The inversion is extremely fast (almost instantaneous), but it requires a one-time preprocessing effort.

Keywords: Root finders; Nonlinear functions; Convergence acceleration; Computational efficiency (search for similar items in EconPapers)
Date: 2018
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Citations: View citations in EconPapers (2)

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Persistent link: https://EconPapers.repec.org/RePEc:eee:apmaco:v:320:y:2018:i:c:p:754-768

DOI: 10.1016/j.amc.2017.10.009

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