{"id":1458,"date":"2025-09-26T10:13:16","date_gmt":"2025-09-26T08:13:16","guid":{"rendered":"https:\/\/dottorati.unica.it\/matematicaeinformatica\/?p=1458"},"modified":"2025-09-26T10:13:16","modified_gmt":"2025-09-26T08:13:16","slug":"phd-course-insights-and-algorithms-for-ill-posed-problems","status":"publish","type":"post","link":"https:\/\/dottorati.unica.it\/matematicaeinformatica\/2025\/09\/26\/phd-course-insights-and-algorithms-for-ill-posed-problems\/","title":{"rendered":"PhD Course: Insights and Algorithms for Ill-Posed Problems"},"content":{"rendered":"<h1>Insights and Algorithms for Ill-Posed Problems<\/h1>\n<p><strong>Prof. Lothar Reichel and Prof. Laura Dykes<\/strong><br \/>\nKent State University, USA<\/p>\n<p><strong>Abstract<\/strong><\/p>\n<p>The aim of this course is to introduce Master&#8217;s and Ph.D. students to linear ill-posed problems. Their properties and applications will be discussed. The focus of the lectures will be on solution methods for linear discrete ill-posed problems and on the numerical linear algebra required for the solution of these problems.<\/p>\n<p>While there are no prerequisites, a basic knowledge of numerical linear algebra, least squares, LU, QR and SVD factorizations, and Matlab programming will be helpful for successfully following the lessons.<\/p>\n<p><strong>Outline<\/strong><\/p>\n<ol>\n<li>Linear discrete ill-posed problems: Definition, properties, applications<\/li>\n<li>Solution methods for small to moderately sized problems: Regularization, Tikhonov regularization, the singular value decomposition, the generalized singular value decomposition, choice of regularization matrix.<\/li>\n<li>Solution methods for large problems: Iterative methods based on the Lanczos process, the Arnoldi process, and Golub-Kahan bidiagonalization. Regularization by Tikhonov&#8217;s method and truncated iteration. Iterative methods for general regularization matrices.<\/li>\n<li>lp-lq minimization for image restoration.<\/li>\n<\/ol>\n<p><strong>Schedule<\/strong><\/p>\n<ul>\n<li>Monday September 29, 15-18, room B<\/li>\n<li>Thursday October 2, 15-18, room 2<\/li>\n<li>Friday October 3, 15-18, room 2<\/li>\n<li>Monday October 6, 15-18, room B<\/li>\n<\/ul>\n<p>The first four lectures will be broadcast on Microsoft Teams for students who cannot attend in person.<\/p>\n<p>The final two lectures, each lasting two hours, will be delivered on Teams after the instructors return to their offices. The schedule will be released during the lectures.<\/p>\n<p>Anyone interested in participating in the course should contact the organizers,\u00a0Alessandro Buccini and Giuseppe Rodriguez.<\/p>\n<p><strong>Exam<\/strong><\/p>\n<p>TBA<\/p>\n<p><strong>Acknowledgements <\/strong><\/p>\n<p>The course is partially supported by the INdAM Visiting Professors Program.<\/p>\n","protected":false},"excerpt":{"rendered":"<p>Insights and Algorithms for Ill-Posed Problems Prof. Lothar Reichel and Prof. Laura Dykes Kent State University, USA Abstract The aim of this course is to introduce Master&#8217;s and Ph.D. students to linear ill-posed problems. Their properties and applications will be discussed. The focus of the lectures will be on solution methods for linear discrete ill-posed problems and on the numerical linear algebra required for the solution of these problems. While there are no prerequisites, a basic knowledge of numerical linear algebra, least squares, LU, QR and SVD factorizations, and Matlab programming will be helpful for successfully following the lessons. Outline <a href='https:\/\/dottorati.unica.it\/matematicaeinformatica\/2025\/09\/26\/phd-course-insights-and-algorithms-for-ill-posed-problems\/' class='excerpt-more'>[&#8230;]<\/a><\/p>\n","protected":false},"author":244,"featured_media":0,"comment_status":"closed","ping_status":"closed","sticky":false,"template":"","format":"standard","meta":{"footnotes":""},"categories":[9,11,10,2],"tags":[],"class_list":["post-1458","post","type-post","status-publish","format-standard","hentry","category-dipartimento-matematica-informatica","category-dottorato-matematica-informatica","category-events","category-news","category-9-id","category-11-id","category-10-id","category-2-id","post-seq-1","post-parity-odd","meta-position-corners","fix"],"_links":{"self":[{"href":"https:\/\/dottorati.unica.it\/matematicaeinformatica\/wp-json\/wp\/v2\/posts\/1458","targetHints":{"allow":["GET"]}}],"collection":[{"href":"https:\/\/dottorati.unica.it\/matematicaeinformatica\/wp-json\/wp\/v2\/posts"}],"about":[{"href":"https:\/\/dottorati.unica.it\/matematicaeinformatica\/wp-json\/wp\/v2\/types\/post"}],"author":[{"embeddable":true,"href":"https:\/\/dottorati.unica.it\/matematicaeinformatica\/wp-json\/wp\/v2\/users\/244"}],"replies":[{"embeddable":true,"href":"https:\/\/dottorati.unica.it\/matematicaeinformatica\/wp-json\/wp\/v2\/comments?post=1458"}],"version-history":[{"count":1,"href":"https:\/\/dottorati.unica.it\/matematicaeinformatica\/wp-json\/wp\/v2\/posts\/1458\/revisions"}],"predecessor-version":[{"id":1459,"href":"https:\/\/dottorati.unica.it\/matematicaeinformatica\/wp-json\/wp\/v2\/posts\/1458\/revisions\/1459"}],"wp:attachment":[{"href":"https:\/\/dottorati.unica.it\/matematicaeinformatica\/wp-json\/wp\/v2\/media?parent=1458"}],"wp:term":[{"taxonomy":"category","embeddable":true,"href":"https:\/\/dottorati.unica.it\/matematicaeinformatica\/wp-json\/wp\/v2\/categories?post=1458"},{"taxonomy":"post_tag","embeddable":true,"href":"https:\/\/dottorati.unica.it\/matematicaeinformatica\/wp-json\/wp\/v2\/tags?post=1458"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}