A new package for nonlinear least squares fitting is introduced in this paper. This package implements a recently developed algorithm that, for certain types of nonlinear curve fitting, reduces the number of nonlinear parameters to be fitted. One notable feature of this method is the absence of initialization which is typically necessary for nonlinear fitting gradient-based algorithms. Instead, just some bounds for the nonlinear parameters are required. Even though convergence for this method is guaranteed for exponential decay using the max-norm, the algorithm exhibits remarkable robustness, and its use has been extended to a wide range of functions using the Euclidean norm. Furthermore, this data-fitting package can also serve as a valuable resource for providing accurate initial parameters to other algorithms that rely on them.
翻译:本文介绍了一种用于非线性最小二乘拟合的新软件包。该软件包实现了一种近期开发的算法,针对特定类型的非线性曲线拟合,可减少待拟合的非线性参数数量。该方法的一个显著特点是不需要初始化,而这在非线性拟合的梯度类算法中通常是必需的,取而代之的仅需给定非线性参数的一些边界。尽管该方法在最大范数下对指数衰减问题具有收敛保证,但该算法展现出显著的鲁棒性,且其应用已拓展至使用欧几里得范数的各类函数。此外,该数据拟合软件包还可为依赖初始参数的其他算法提供精确的初值,从而成为有价值的工具。