不对称中的奇妙和谐Filbert和Lilbert矩阵的非线性变体

IF 0.7 4区数学 Q2 MATHEMATICS

Hacettepe Journal of Mathematics and Statistics Pub Date : 2023-07-30 DOI:10.15672/hujms.1264983

Didem ERSANLI, Emrah KILIÇ

{"title":"不对称中的奇妙和谐Filbert和Lilbert矩阵的非线性变体","authors":"Didem ERSANLI, Emrah KILIÇ","doi":"10.15672/hujms.1264983","DOIUrl":null,"url":null,"abstract":"In this paper, we present a new analogue of the Filbert and Lilbert matrices whose the indices have different asymmetric and nonlinear rules according to their row numbers. Explicit formulæ are derived for the LU-decompositions, their inverses and the inverse of main matrix as well as its determinant. To prove the claimed results we use backward induction method. The asymmetric variants of the Filbert and Lilbert matrices are obtained from our results for a particular q value.","PeriodicalId":55078,"journal":{"name":"Hacettepe Journal of Mathematics and Statistics","volume":"1 1","pages":"0"},"PeriodicalIF":0.7000,"publicationDate":"2023-07-30","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":"0","resultStr":"{\"title\":\"Curious harmony in asymmetric & nonlinear variant of Filbert and Lilbert matrices\",\"authors\":\"Didem ERSANLI, Emrah KILIÇ\",\"doi\":\"10.15672/hujms.1264983\",\"DOIUrl\":null,\"url\":null,\"abstract\":\"In this paper, we present a new analogue of the Filbert and Lilbert matrices whose the indices have different asymmetric and nonlinear rules according to their row numbers. Explicit formulæ are derived for the LU-decompositions, their inverses and the inverse of main matrix as well as its determinant. To prove the claimed results we use backward induction method. The asymmetric variants of the Filbert and Lilbert matrices are obtained from our results for a particular q value.\",\"PeriodicalId\":55078,\"journal\":{\"name\":\"Hacettepe Journal of Mathematics and Statistics\",\"volume\":\"1 1\",\"pages\":\"0\"},\"PeriodicalIF\":0.7000,\"publicationDate\":\"2023-07-30\",\"publicationTypes\":\"Journal Article\",\"fieldsOfStudy\":null,\"isOpenAccess\":false,\"openAccessPdf\":\"\",\"citationCount\":\"0\",\"resultStr\":null,\"platform\":\"Semanticscholar\",\"paperid\":null,\"PeriodicalName\":\"Hacettepe Journal of Mathematics and Statistics\",\"FirstCategoryId\":\"1085\",\"ListUrlMain\":\"https://doi.org/10.15672/hujms.1264983\",\"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":"1085","ListUrlMain":"https://doi.org/10.15672/hujms.1264983","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

本文给出了Filbert和Lilbert矩阵的一种新的类似矩阵，它们的指标根据行数的不同具有不同的非对称和非线性规则。导出了主矩阵的lu分解及其逆、主矩阵的逆及其行列式的显式公式。为了证明所宣称的结果，我们使用了逆向归纳法。从我们的结果中得到了特定q值下Filbert和Lilbert矩阵的非对称变体。

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

Curious harmony in asymmetric & nonlinear variant of Filbert and Lilbert matrices

In this paper, we present a new analogue of the Filbert and Lilbert matrices whose the indices have different asymmetric and nonlinear rules according to their row numbers. Explicit formulæ are derived for the LU-decompositions, their inverses and the inverse of main matrix as well as its determinant. To prove the claimed results we use backward induction method. The asymmetric variants of the Filbert and Lilbert matrices are obtained from our results for a particular q value.

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.