A program for the solution of ill-posed linear systems arising from the discretization of the Fredholm integral equation of the first kind

Abstract
A computer program written in FORTRAN IV for obtaining smooth solutions of ill-posed systems of linear equations arising from the discretization of the Fredholm integral equation of the first kind is given. It is based on a novel algorithm by the author. The algorithm is iterative using linear programming techniques and is numerically stable. Numerical results show that it gives accuracy comparable to the truncated singular value decomposition method, yet it is about 2 to 5 times faster. The ...

Title of program: MLS
Catalogue Id: ABLZ_v1_0

Nature of problem
Fredholm integral equation of the first kind arises in the mathematical analysis of many physical problems. Among these are in optics, the restoration of blurred images.

Versions of this program held in the CPC repository in Mendeley Data
ABLZ_v1_0; MLS; 10.1016/0010-4655(90)90064-8

This program has been imported from the CPC Program Library held at Queen's University Belfast (1969-2019)

摘要：本节阐述了一种基于FORTRAN IV编写的计算机程序，旨在获取由Fredholm一类积分方程离散化所引发的病态线性方程组的平滑解。该程序基于作者提出的创新算法。算法采用迭代方式，结合线性规划技术，具备数值稳定性。数值结果显示，该算法的精度可与截断奇异值分解法相媲美，同时其运算速度约为后者的2至5倍。...

程序标题：MLS
目录编号：ABLZ_v1_0

问题性质：一类Fredholm积分方程在众多物理问题的数学分析中均有出现。其中，光学领域图像的模糊恢复便是其应用之一。

本程序版本存放在Mendeley Data中的CPC程序库：ABLZ_v1_0；MLS；10.1016/0010-4655(90)90064-8

该程序已从贝尔法斯特女王大学（1969-2019）所持有的CPC程序库中导入。