Conditioning Theory for ML-Weighted Pseudoinverse and ML-Weighted Least Squares Problem

IF 16.4 1区化学 Q1 CHEMISTRY, MULTIDISCIPLINARY

Accounts of Chemical Research Pub Date : 2024-05-22 DOI:10.3390/axioms13060345

Mahvish Samar, Xinzhong Zhu, Huiying Xu

引用次数: 0

Abstract

The conditioning theory of the ML-weighted least squares and ML-weighted pseudoinverse problems is explored in this article. We begin by introducing three types of condition numbers for the ML-weighted pseudoinverse problem: normwise, mixed, and componentwise, along with their explicit expressions. Utilizing the derivative of the ML-weighted pseudoinverse problem, we then provide explicit condition number expressions for the solution of the ML-weighted least squares problem. To ensure reliable estimation of these condition numbers, we employ the small-sample statistical condition estimation method for all three algorithms. The article concludes with numerical examples that highlight the results obtained.

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ML 加权伪逆和 ML 加权最小二乘法问题的条件理论

本文探讨了 ML 加权最小二乘法和 ML 加权伪逆问题的条件理论。首先，我们介绍了 ML 加权伪逆问题的三种条件数：规范数、混合数和分量数，以及它们的明确表达式。然后，我们利用 ML 加权伪逆问题的导数，为 ML 加权最小二乘问题的求解提供了明确的条件数表达式。为了确保可靠地估计这些条件数，我们对所有三种算法都采用了小样本统计条件估计方法。文章最后以数值示例强调了所获得的结果。

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

Accounts of Chemical Research 化学-化学综合

CiteScore

31.40

自引率

1.10%

发文量

312

审稿时长

2 months

期刊介绍： Accounts of Chemical Research presents short, concise and critical articles offering easy-to-read overviews of basic research and applications in all areas of chemistry and biochemistry. These short reviews focus on research from the author’s own laboratory and are designed to teach the reader about a research project. In addition, Accounts of Chemical Research publishes commentaries that give an informed opinion on a current research problem. Special Issues online are devoted to a single topic of unusual activity and significance. Accounts of Chemical Research replaces the traditional article abstract with an article "Conspectus." These entries synopsize the research affording the reader a closer look at the content and significance of an article. Through this provision of a more detailed description of the article contents, the Conspectus enhances the article's discoverability by search engines and the exposure for the research.