OPTIMAL K-VECTOR TO INVERT NONLINEAR FUNCTIONS Conference Paper uri icon

abstract

  • This work proposes a numerical technique that can be used to invert one dimensional analytic or tabulated nonlinear functions in assigned ranges of interest. The approach proposed is based on an "optimal" version of the k-vector range searching technique. The optimality consists of retrieving a prescribed number of data (1, 2, ) to initiate the root solver. This allows flexibility to adopt a variety of root solvers (bisection, Newton, regula falsi, etc.) to obtain machine error precision. The method is suitable when extensive inversions of the same function must be done, as for instance to build an inverse function toolbox. The method is extremely fast, but it requires a one-time preprocessing effort for each distinct nonlinear function and range of interest. This method can be also applied to provide inversion estimates of tabulated data of unknown functions. Numerical examples are provided for some nonlinear analytic and tabulated functions.

author list (cited authors)

  • Arnas, D., & Mortari, D.

publication date

  • January 2017