{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2025,5,14]],"date-time":"2025-05-14T02:41:39Z","timestamp":1747190499394,"version":"3.40.5"},"reference-count":22,"publisher":"Wiley","license":[{"start":{"date-parts":[[2021,11,26]],"date-time":"2021-11-26T00:00:00Z","timestamp":1637884800000},"content-version":"unspecified","delay-in-days":0,"URL":"https:\/\/creativecommons.org\/licenses\/by\/4.0\/"}],"content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["Journal of Applied Mathematics"],"published-print":{"date-parts":[[2021,11,26]]},"abstract":"<jats:p>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 <jats:inline-formula>\n                     <a:math xmlns:a=\"http:\/\/www.w3.org\/1998\/Math\/MathML\" id=\"M1\">\n                        <a:mi>\u03ba<\/a:mi>\n                        <a:mfenced open=\"(\" close=\")\">\n                           <a:mrow>\n                              <a:mi>K<\/a:mi>\n                           <\/a:mrow>\n                        <\/a:mfenced>\n                        <a:mo>=<\/a:mo>\n                        <a:mfenced open=\"\u2016\" close=\"\u2016\">\n                           <a:mrow>\n                              <a:msup>\n                                 <a:mrow>\n                                    <a:mi>K<\/a:mi>\n                                 <\/a:mrow>\n                                 <a:mrow>\n                                    <a:mo>\u2212<\/a:mo>\n                                    <a:mn>1<\/a:mn>\n                                 <\/a:mrow>\n                              <\/a:msup>\n                              <a:mi>K<\/a:mi>\n                           <\/a:mrow>\n                        <\/a:mfenced>\n                        <a:mo>=<\/a:mo>\n                        <a:mn>1<\/a:mn>\n                     <\/a:math>\n                  <\/jats:inline-formula>. Thus, the condition number of ESRM is bounded by unity, unlike the other regularization methods such as SVDM, GLSM, CDM, and QRFM.<\/jats:p>","DOI":"10.1155\/2021\/4373290","type":"journal-article","created":{"date-parts":[[2021,11,27]],"date-time":"2021-11-27T02:20:15Z","timestamp":1637979615000},"page":"1-11","source":"Crossref","is-referenced-by-count":0,"title":["The Eigenspace Spectral Regularization Method for Solving Discrete Ill-Posed Systems"],"prefix":"10.1155","volume":"2021","author":[{"ORCID":"https:\/\/orcid.org\/0000-0002-1146-8819","authenticated-orcid":true,"given":"Fredrick Asenso","family":"Wireko","sequence":"first","affiliation":[{"name":"Mathematics Department, Kwame Nkrumah University of Science and Technology, Ghana"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"ORCID":"https:\/\/orcid.org\/0000-0002-0580-5655","authenticated-orcid":true,"given":"Benedict","family":"Barnes","sequence":"additional","affiliation":[{"name":"Mathematics Department, Kwame Nkrumah University of Science and Technology, Ghana"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Charles","family":"Sebil","sequence":"additional","affiliation":[{"name":"Mathematics Department, Kwame Nkrumah University of Science and Technology, Ghana"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Joseph","family":"Ackora-Prah","sequence":"additional","affiliation":[{"name":"Mathematics Department, Kwame Nkrumah University of Science and Technology, Ghana"}],"role":[{"role":"author","vocabulary":"crossref"}]}],"member":"311","reference":[{"key":"1","doi-asserted-by":"publisher","DOI":"10.1515\/9783110224016"},{"volume-title":"Well-posed, ill-posed, and intermediate problems with applications","year":"2011","author":"S. 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