Structure of the least square solutions to overdetermined systems and its applications to practical inverse problems

IF 0.7 4区数学 Q3 MATHEMATICS, APPLIED

Japan Journal of Industrial and Applied Mathematics Pub Date : 2024-03-05 DOI:10.1007/s13160-023-00640-4

引用次数: 0

Abstract

In this paper, we study the structure of the least square solutions to overdetermined systems with no solution. In the main theorem, we prove that if an overdetermined system with no solution is deformed into a system of linear equations by the semi-equivalent deformations defined in this paper, then an approximate solution to the original overdetermined system with no solution can be given as the unique least square solution to the deformed system of linear equations. We also introduce some applications of our main theorem to practical inverse problems.

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超定系统最小平方解的结构及其在实际逆问题中的应用

摘要本文研究了无解超定系统最小平方解的结构。在主定理中，我们证明了如果用本文定义的半等价变形将无解超定系统变形为线性方程组，那么原始无解超定系统的近似解可以作为变形线性方程组的唯一最小平方解给出。我们还介绍了我们的主定理在实际逆问题中的一些应用。

本文章由计算机程序翻译，如有差异，请以英文原文为准。

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来源期刊

Japan Journal of Industrial and Applied Mathematics 数学-应用数学

CiteScore

1.50

自引率

11.10%

发文量

审稿时长

>12 weeks

期刊介绍： Japan Journal of Industrial and Applied Mathematics (JJIAM) is intended to provide an international forum for the expression of new ideas, as well as a site for the presentation of original research in various fields of the mathematical sciences. Consequently the most welcome types of articles are those which provide new insights into and methods for mathematical structures of various phenomena in the natural, social and industrial sciences, those which link real-world phenomena and mathematics through modeling and analysis, and those which impact the development of the mathematical sciences. The scope of the journal covers applied mathematical analysis, computational techniques and industrial mathematics.