The Eigenspace Spectral Regularization Method for Solving Discrete Ill-Posed Systems

Fredrick Asenso Wireko, Benedict Barnes, Charles Sebil, Joseph Ackora-Prah and Nazim I. Mahmudov

Journal of Applied Mathematics, 2021, vol. 2021, 1-11

Abstract: 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.

Date: 2021
References: Add references at CitEc
Citations:

Downloads: (external link)
http://downloads.hindawi.com/journals/jam/4373290.pdf (application/pdf)
http://downloads.hindawi.com/journals/jam/4373290.xml (application/xml)

Related works:
This item may be available elsewhere in EconPapers: Search for items with the same title.

Export reference: BibTeX RIS (EndNote, ProCite, RefMan) HTML/Text

Persistent link: https://EconPapers.repec.org/RePEc:hin:jnljam:4373290

DOI: 10.1155/2021/4373290

Access Statistics for this article

More articles in Journal of Applied Mathematics from Hindawi
Bibliographic data for series maintained by Mohamed Abdelhakeem ().