Iterative method for solving linear operator equation of the first kind
In this work, we study the iterative method for solving linear operator equation of the first kind. We present a new version of method based on the applied the iterative performance on the modified Lavrentiev method. This method is used to resolve a linear operator problem of the first kind. The sug...
| Main Authors: | , , , |
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| Format: | Article |
| Language: | English |
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Elsevier
2023-01-01
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| Series: | MethodsX |
| Subjects: | |
| Online Access: | http://www.sciencedirect.com/science/article/pii/S221501612300208X |
| _version_ | 1797796405263204352 |
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| author | Salam Abdulkhaleq Noaman H.K. Al-Mahdawi Bashar Talib Al-Nuaimi A.I. Sidikova |
| author_facet | Salam Abdulkhaleq Noaman H.K. Al-Mahdawi Bashar Talib Al-Nuaimi A.I. Sidikova |
| author_sort | Salam Abdulkhaleq Noaman |
| collection | DOAJ |
| description | In this work, we study the iterative method for solving linear operator equation of the first kind. We present a new version of method based on the applied the iterative performance on the modified Lavrentiev method. This method is used to resolve a linear operator problem of the first kind. The suggested iterative can used to compute approximate solutions with high quality than the (standard) modified Lavrentiev regularization method. We also compared the new iterative method (modified Lavrentiev) with Landweber iterative method. The numerical testing shows the efficiency of the new iterative method in its application to resolve the inverse heat equation when trying to find the boundary value function. • Studying of new iteration algorithm and mathematical experimentations show the efficiency of the new iteration method. • Iteration method is depended on decomposed the main linear operator by using polar decomposition in order to obtain unitary operator. • The new unitary operator increases the convergence of iteration. |
| first_indexed | 2024-03-13T03:32:35Z |
| format | Article |
| id | doaj.art-8bfa1c39abba429d9db879cbdb2c2e79 |
| institution | Directory Open Access Journal |
| issn | 2215-0161 |
| language | English |
| last_indexed | 2024-03-13T03:32:35Z |
| publishDate | 2023-01-01 |
| publisher | Elsevier |
| record_format | Article |
| series | MethodsX |
| spelling | doaj.art-8bfa1c39abba429d9db879cbdb2c2e792023-06-24T05:17:44ZengElsevierMethodsX2215-01612023-01-0110102210Iterative method for solving linear operator equation of the first kindSalam Abdulkhaleq Noaman0H.K. Al-Mahdawi1Bashar Talib Al-Nuaimi2A.I. Sidikova3University of Diyala, Diyala 32001, IraqUniversity of Diyala, Diyala 32001, Iraq; Corresponding author.University of Diyala, Diyala 32001, IraqDepartment of System Programming, South Ural State University, Chelyabinsk 454080, RussiaIn this work, we study the iterative method for solving linear operator equation of the first kind. We present a new version of method based on the applied the iterative performance on the modified Lavrentiev method. This method is used to resolve a linear operator problem of the first kind. The suggested iterative can used to compute approximate solutions with high quality than the (standard) modified Lavrentiev regularization method. We also compared the new iterative method (modified Lavrentiev) with Landweber iterative method. The numerical testing shows the efficiency of the new iterative method in its application to resolve the inverse heat equation when trying to find the boundary value function. • Studying of new iteration algorithm and mathematical experimentations show the efficiency of the new iteration method. • Iteration method is depended on decomposed the main linear operator by using polar decomposition in order to obtain unitary operator. • The new unitary operator increases the convergence of iteration.http://www.sciencedirect.com/science/article/pii/S221501612300208XIterative Method |
| spellingShingle | Salam Abdulkhaleq Noaman H.K. Al-Mahdawi Bashar Talib Al-Nuaimi A.I. Sidikova Iterative method for solving linear operator equation of the first kind MethodsX Iterative Method |
| title | Iterative method for solving linear operator equation of the first kind |
| title_full | Iterative method for solving linear operator equation of the first kind |
| title_fullStr | Iterative method for solving linear operator equation of the first kind |
| title_full_unstemmed | Iterative method for solving linear operator equation of the first kind |
| title_short | Iterative method for solving linear operator equation of the first kind |
| title_sort | iterative method for solving linear operator equation of the first kind |
| topic | Iterative Method |
| url | http://www.sciencedirect.com/science/article/pii/S221501612300208X |
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