内-gMP 和 gMP-内倒数

IF 0.7 4区数学 Q2 MATHEMATICS

Hacettepe Journal of Mathematics and Statistics Pub Date : 2024-01-10 DOI:10.15672/hujms.1351762

Dunja Stojanovi̇c, D. Mosić

{"title":"内-gMP 和 gMP-内倒数","authors":"Dunja Stojanovi̇c, D. Mosić","doi":"10.15672/hujms.1351762","DOIUrl":null,"url":null,"abstract":"Solving some systems of operator equations, new kinds of generalized inverses are introduced. \nSince these new inverses can be expressed by inner and gMP inverses, they are called inner-gMP and gMP-inner inverses. \nIn this way, the concepts of gMP, 1MP and MP1 inverses are generalized. Various representations and characterizations of inner-gMP and gMP-inner inverses are presented. Using the inner and *gMP inverse, we define the inner-*gMP and *gMP-inner inverses which are new extensions of 1MP, MP1 and *gMP inverses. \nWe apply inner-gMP and gMP-inner inverses as well as inner-*gMP and *gMP-inner inverses to solve several kinds of linear equations. Consequently, we obtain solvability of the normal equation which is connected to the least--squares solution. Numerical examples are given to illustrate our results.","PeriodicalId":55078,"journal":{"name":"Hacettepe Journal of Mathematics and Statistics","volume":"92 9","pages":""},"PeriodicalIF":0.7000,"publicationDate":"2024-01-10","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":"0","resultStr":"{\"title\":\"Inner-gMP and gMP-inner inverses\",\"authors\":\"Dunja Stojanovi̇c, D. Mosić\",\"doi\":\"10.15672/hujms.1351762\",\"DOIUrl\":null,\"url\":null,\"abstract\":\"Solving some systems of operator equations, new kinds of generalized inverses are introduced. \\nSince these new inverses can be expressed by inner and gMP inverses, they are called inner-gMP and gMP-inner inverses. \\nIn this way, the concepts of gMP, 1MP and MP1 inverses are generalized. Various representations and characterizations of inner-gMP and gMP-inner inverses are presented. Using the inner and *gMP inverse, we define the inner-*gMP and *gMP-inner inverses which are new extensions of 1MP, MP1 and *gMP inverses. \\nWe apply inner-gMP and gMP-inner inverses as well as inner-*gMP and *gMP-inner inverses to solve several kinds of linear equations. Consequently, we obtain solvability of the normal equation which is connected to the least--squares solution. Numerical examples are given to illustrate our results.\",\"PeriodicalId\":55078,\"journal\":{\"name\":\"Hacettepe Journal of Mathematics and Statistics\",\"volume\":\"92 9\",\"pages\":\"\"},\"PeriodicalIF\":0.7000,\"publicationDate\":\"2024-01-10\",\"publicationTypes\":\"Journal Article\",\"fieldsOfStudy\":null,\"isOpenAccess\":false,\"openAccessPdf\":\"\",\"citationCount\":\"0\",\"resultStr\":null,\"platform\":\"Semanticscholar\",\"paperid\":null,\"PeriodicalName\":\"Hacettepe Journal of Mathematics and Statistics\",\"FirstCategoryId\":\"100\",\"ListUrlMain\":\"https://doi.org/10.15672/hujms.1351762\",\"RegionNum\":4,\"RegionCategory\":\"数学\",\"ArticlePicture\":[],\"TitleCN\":null,\"AbstractTextCN\":null,\"PMCID\":null,\"EPubDate\":\"\",\"PubModel\":\"\",\"JCR\":\"Q2\",\"JCRName\":\"MATHEMATICS\",\"Score\":null,\"Total\":0}","platform":"Semanticscholar","paperid":null,"PeriodicalName":"Hacettepe Journal of Mathematics and Statistics","FirstCategoryId":"100","ListUrlMain":"https://doi.org/10.15672/hujms.1351762","RegionNum":4,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"","PubModel":"","JCR":"Q2","JCRName":"MATHEMATICS","Score":null,"Total":0}

引用次数: 0

摘要

在求解某些算子方程组时，会引入新的广义逆。由于这些新的逆运算可以用内逆运算和 gMP 逆运算来表示，因此被称为内-gMP 逆运算和 gMP-inner 逆运算。这样，gMP、1MP 和 MP1 逆变换的概念就得到了推广。本文介绍了 inner-gMP 和 gMP-inner 逆的各种表示方法和特征。利用内gMP逆和*gMP逆，我们定义了内*gMP逆和*gMP-内逆，它们是1MP、MP1和*gMP逆的新扩展。我们应用 inner-gMP 和 gMP-inner 逆，以及 inner-*gMP 和 *gMP-inner 逆来求解几种线性方程。因此，我们获得了与最小二乘法求解相关的正则方程的可解性。我们给出了一些数值例子来说明我们的结果。

本文章由计算机程序翻译，如有差异，请以英文原文为准。

查看原文本刊更多论文

Inner-gMP and gMP-inner inverses

Solving some systems of operator equations, new kinds of generalized inverses are introduced. Since these new inverses can be expressed by inner and gMP inverses, they are called inner-gMP and gMP-inner inverses. In this way, the concepts of gMP, 1MP and MP1 inverses are generalized. Various representations and characterizations of inner-gMP and gMP-inner inverses are presented. Using the inner and *gMP inverse, we define the inner-*gMP and *gMP-inner inverses which are new extensions of 1MP, MP1 and *gMP inverses. We apply inner-gMP and gMP-inner inverses as well as inner-*gMP and *gMP-inner inverses to solve several kinds of linear equations. Consequently, we obtain solvability of the normal equation which is connected to the least--squares solution. Numerical examples are given to illustrate our results.

求助全文

通过发布文献求助，成功后即可免费获取论文全文。去求助

来源期刊

Hacettepe Journal of Mathematics and Statistics 数学-数学

CiteScore

1.70

自引率

0.00%

发文量

100

审稿时长

6-12 weeks

期刊介绍： Hacettepe Journal of Mathematics and Statistics covers all aspects of Mathematics and Statistics. Papers on the interface between Mathematics and Statistics are particularly welcome, including applications to Physics, Actuarial Sciences, Finance and Economics. We strongly encourage submissions for Statistics Section including current and important real world examples across a wide range of disciplines. Papers have innovations of statistical methodology are highly welcome. Purely theoretical papers may be considered only if they include popular real world applications.