Structured conditioning theory for the total least squares problem with linear equality constraint and their estimation
This article is devoted to the structured and unstructured condition numbers for the total least squares with linear equality constraint (TLSE) problem. By making use of the dual techniques, we investigate three distinct kinds of unstructured condition numbers for a linear function of the TLSE solut...
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| Format: | Article |
| Language: | English |
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AIMS Press
2023-03-01
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| Series: | AIMS Mathematics |
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| Online Access: | https://www.aimspress.com/article/doi/10.3934/math.2023575?viewType=HTML |
| _version_ | 1797861288792031232 |
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| author | Mahvish Samar Xinzhong Zhu |
| author_facet | Mahvish Samar Xinzhong Zhu |
| author_sort | Mahvish Samar |
| collection | DOAJ |
| description | This article is devoted to the structured and unstructured condition numbers for the total least squares with linear equality constraint (TLSE) problem. By making use of the dual techniques, we investigate three distinct kinds of unstructured condition numbers for a linear function of the TLSE solution and three structured condition numbers for this problem, i.e., normwise, mixed, and componentwise ones, and present their explicit expressions under both unstructured and structured componentwise perturbations. In addition, the relations between structured and unstructured normwise, componentwise, and mixed condition numbers for the TLSE problem are investigated. Furthermore, using the small-sample statistical condition estimation method, we also consider the statistical estimation of both unstructured and structured condition numbers and propose three algorithms. Theoretical and experimental results show that structured condition numbers are always smaller than the corresponding unstructured condition numbers. |
| first_indexed | 2024-04-09T21:59:49Z |
| format | Article |
| id | doaj.art-7d08e135a7d642a1a8d71f4639518efe |
| institution | Directory Open Access Journal |
| issn | 2473-6988 |
| language | English |
| last_indexed | 2024-04-09T21:59:49Z |
| publishDate | 2023-03-01 |
| publisher | AIMS Press |
| record_format | Article |
| series | AIMS Mathematics |
| spelling | doaj.art-7d08e135a7d642a1a8d71f4639518efe2023-03-24T01:27:00ZengAIMS PressAIMS Mathematics2473-69882023-03-0185113501137210.3934/math.2023575Structured conditioning theory for the total least squares problem with linear equality constraint and their estimationMahvish Samar0Xinzhong Zhu 11. College of Mathematics and Computer Science, Zhejiang Normal University, Jinhua 321004, China1. College of Mathematics and Computer Science, Zhejiang Normal University, Jinhua 321004, China 2. AI Research Institute of Beijing Geekplus Technology Co., Ltd., Beijing 100101, ChinaThis article is devoted to the structured and unstructured condition numbers for the total least squares with linear equality constraint (TLSE) problem. By making use of the dual techniques, we investigate three distinct kinds of unstructured condition numbers for a linear function of the TLSE solution and three structured condition numbers for this problem, i.e., normwise, mixed, and componentwise ones, and present their explicit expressions under both unstructured and structured componentwise perturbations. In addition, the relations between structured and unstructured normwise, componentwise, and mixed condition numbers for the TLSE problem are investigated. Furthermore, using the small-sample statistical condition estimation method, we also consider the statistical estimation of both unstructured and structured condition numbers and propose three algorithms. Theoretical and experimental results show that structured condition numbers are always smaller than the corresponding unstructured condition numbers.https://www.aimspress.com/article/doi/10.3934/math.2023575?viewType=HTMLtotal least squares problem with linear equality constraintstructured condition numbersunstructured condition numbers |
| spellingShingle | Mahvish Samar Xinzhong Zhu Structured conditioning theory for the total least squares problem with linear equality constraint and their estimation AIMS Mathematics total least squares problem with linear equality constraint structured condition numbers unstructured condition numbers |
| title | Structured conditioning theory for the total least squares problem with linear equality constraint and their estimation |
| title_full | Structured conditioning theory for the total least squares problem with linear equality constraint and their estimation |
| title_fullStr | Structured conditioning theory for the total least squares problem with linear equality constraint and their estimation |
| title_full_unstemmed | Structured conditioning theory for the total least squares problem with linear equality constraint and their estimation |
| title_short | Structured conditioning theory for the total least squares problem with linear equality constraint and their estimation |
| title_sort | structured conditioning theory for the total least squares problem with linear equality constraint and their estimation |
| topic | total least squares problem with linear equality constraint structured condition numbers unstructured condition numbers |
| url | https://www.aimspress.com/article/doi/10.3934/math.2023575?viewType=HTML |
| work_keys_str_mv | AT mahvishsamar structuredconditioningtheoryforthetotalleastsquaresproblemwithlinearequalityconstraintandtheirestimation AT xinzhongzhu structuredconditioningtheoryforthetotalleastsquaresproblemwithlinearequalityconstraintandtheirestimation |