The Eigenspace Spectral Regularization Method for Solving Discrete Ill-Posed Systems
This paper shows that discrete linear equations with Hilbert matrix operator, circulant matrix operator, conference matrix operator, banded matrix operator, TST matrix operator, and sparse matrix operator are ill-posed in the sense of Hadamard. Gauss least square method (GLSM), QR factorization meth...
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| Main Authors: | , , , |
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| Format: | Article |
| Language: | English |
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Wiley
2021-01-01
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| Series: | Journal of Applied Mathematics |
| Online Access: | http://dx.doi.org/10.1155/2021/4373290 |
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| _version_ | 1832547933001613312 |
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| author | Fredrick Asenso Wireko Benedict Barnes Charles Sebil Joseph Ackora-Prah |
| author_facet | Fredrick Asenso Wireko Benedict Barnes Charles Sebil Joseph Ackora-Prah |
| author_sort | Fredrick Asenso Wireko |
| collection | DOAJ |
| description | This paper shows that discrete linear equations with Hilbert matrix operator, circulant matrix operator, conference matrix operator, banded matrix operator, TST matrix operator, and sparse matrix operator are ill-posed in the sense of Hadamard. Gauss least square method (GLSM), QR factorization method (QRFM), Cholesky decomposition method (CDM), and singular value decomposition (SVDM) failed to regularize these ill-posed problems. This paper introduces the eigenspace spectral regularization method (ESRM), which solves ill-posed discrete equations with Hilbert matrix operator, circulant matrix operator, conference matrix operator, and banded and sparse matrix operator. Unlike GLSM, QRFM, CDM, and SVDM, the ESRM regularizes such a system. In addition, the ESRM has a unique property, the norm of the eigenspace spectral matrix operator κK=K−1K=1. Thus, the condition number of ESRM is bounded by unity, unlike the other regularization methods such as SVDM, GLSM, CDM, and QRFM. |
| format | Article |
| id | doaj-art-94633957d96944cfa9628e77336a2e54 |
| institution | Kabale University |
| issn | 1687-0042 |
| language | English |
| publishDate | 2021-01-01 |
| publisher | Wiley |
| record_format | Article |
| series | Journal of Applied Mathematics |
| spelling | doaj-art-94633957d96944cfa9628e77336a2e542025-02-03T06:42:51ZengWileyJournal of Applied Mathematics1687-00422021-01-01202110.1155/2021/4373290The Eigenspace Spectral Regularization Method for Solving Discrete Ill-Posed SystemsFredrick Asenso Wireko0Benedict Barnes1Charles Sebil2Joseph Ackora-Prah3Mathematics DepartmentMathematics DepartmentMathematics DepartmentMathematics DepartmentThis paper shows that discrete linear equations with Hilbert matrix operator, circulant matrix operator, conference matrix operator, banded matrix operator, TST matrix operator, and sparse matrix operator are ill-posed in the sense of Hadamard. Gauss least square method (GLSM), QR factorization method (QRFM), Cholesky decomposition method (CDM), and singular value decomposition (SVDM) failed to regularize these ill-posed problems. This paper introduces the eigenspace spectral regularization method (ESRM), which solves ill-posed discrete equations with Hilbert matrix operator, circulant matrix operator, conference matrix operator, and banded and sparse matrix operator. Unlike GLSM, QRFM, CDM, and SVDM, the ESRM regularizes such a system. In addition, the ESRM has a unique property, the norm of the eigenspace spectral matrix operator κK=K−1K=1. Thus, the condition number of ESRM is bounded by unity, unlike the other regularization methods such as SVDM, GLSM, CDM, and QRFM.http://dx.doi.org/10.1155/2021/4373290 |
| spellingShingle | Fredrick Asenso Wireko Benedict Barnes Charles Sebil Joseph Ackora-Prah The Eigenspace Spectral Regularization Method for Solving Discrete Ill-Posed Systems Journal of Applied Mathematics |
| title | The Eigenspace Spectral Regularization Method for Solving Discrete Ill-Posed Systems |
| title_full | The Eigenspace Spectral Regularization Method for Solving Discrete Ill-Posed Systems |
| title_fullStr | The Eigenspace Spectral Regularization Method for Solving Discrete Ill-Posed Systems |
| title_full_unstemmed | The Eigenspace Spectral Regularization Method for Solving Discrete Ill-Posed Systems |
| title_short | The Eigenspace Spectral Regularization Method for Solving Discrete Ill-Posed Systems |
| title_sort | eigenspace spectral regularization method for solving discrete ill posed systems |
| url | http://dx.doi.org/10.1155/2021/4373290 |
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