A regularization method for nonlinear ill-posed problems

Abstract Often, physically interesting functions are not directly accessible by an experiment, and must be calculated from data of an experimental accessible quantity. If this calculation requires the inversion of a Fredholm integral equation of the first kind, the determination of the physically interesting function is an ill-posed problem. In this case, linear regularization methods should be used to perform the calculations. However, in several applications the relation between the interesting func... Title of program: NLREG Catalogue Id: ACGH_v2_0 [ACPF] Nature of problem Physically interesting functions are often not directly accessible by an experiment, and must be calculated from data of an experimental accessible quantity. In many cases this calculation requires the inversion of a nonlinear integral equation, and a nonlinear regularization method should be applied. Versions of this program held in the CPC repository in Mendeley Data ACGH_v1_0; FTIKREG; 10.1016/0010-4655(92)90132-I ACGH_v2_0; NLREG; 10.1016/0010-4655(93)90187-H ACGH_v3_0; GENEREG; 10.1016/S0010-4655(01)00217-X This program has been imported from the CPC Program Library held at Queen's University Belfast (1969-2019)摘要：在多数科研场景中，物理层面具有研究价值的函数无法通过实验直接获取，需从实验可测物理量的原始数据中推导计算得到。若该推导过程需要求解第一类弗雷德霍姆（Fredholm）积分方程的逆问题，则确定目标物理函数的任务属于不适定问题，此时应采用线性正则化方法完成计算。但在部分实际应用中，目标函数与 程序名称：NLREG 目录编号：ACGH_v2_0 [ACPF] 问题本质：物理上具有研究价值的函数通常无法通过实验直接测得，需由实验可采集的物理量数据计算得到。在多数情况下，该计算过程需要求解非线性积分方程的逆问题，因此需采用非线性正则化方法进行处理。 该程序在Mendeley数据平台的CPC程序库中的版本如下： ACGH_v1_0；FTIKREG；10.1016/0010-4655(92)90132-I ACGH_v2_0；NLREG；10.1016/0010-4655(93)90187-H ACGH_v3_0；GENEREG；10.1016/S0010-4655(01)00217-X 本程序源自贝尔法斯特女王大学馆藏的CPC程序库（1969-2019）