论文标题
使用k-vector的非线性函数反转
Nonlinear Function Inversion using k-vector
论文作者
论文摘要
这项工作引入了一种通用数值技术，可以在分配的感兴趣范围内倒入一维分析或表格的非线性函数。所提出的方法基于K-Vector范围搜索的最佳版本，这是为函数反转设计的临时修改。最优性包括检索指定的搜索范围以启动根求解器的始终与相同数量的数据（$ 1,2，\ DOTS $）组成。这提供了使用指定数量的起点的灵活性，以使技术适应各种根求解器（例如，分配，牛顿等）。所提出的方法允许为一组指定的非线性函数构建一个反函数工具箱。特别是，当需要相同函数的密集反转时，该方法是合适的。反转非常快（几乎瞬时），但需要一次性的预处理。
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 ($1,2,\dots$) 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.
