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Nonlinear function inversion using k-vector
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DOI：10.1016/j.amc.2017.10.009.png)
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Abstract
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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. (C) 2017 Elsevier Inc. All rights reserved.
Keywords:
Root finders
Nonlinear functions
Convergence acceleration
Computational efficiency
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