{"id":4531,"date":"2022-05-04T10:01:39","date_gmt":"2022-05-04T08:01:39","guid":{"rendered":"https:\/\/www.dm.unipi.it\/eventi\/on-the-positive-definite-solution-of-the-nonlinear-matrix-equation-xpamtxbm-jie-meng-pusan-national-university\/"},"modified":"2022-05-04T10:01:39","modified_gmt":"2022-05-04T08:01:39","slug":"on-the-positive-definite-solution-of-the-nonlinear-matrix-equation-xpamtxbm-jie-meng-pusan-national-university","status":"publish","type":"unipievents","link":"https:\/\/www.dm.unipi.it\/en\/eventi\/on-the-positive-definite-solution-of-the-nonlinear-matrix-equation-xpamtxbm-jie-meng-pusan-national-university\/","title":{"rendered":"On the positive definite solution of the nonlinear matrix equation X^p=A+M^T(X#B)M &#8211; Jie Meng (Pusan National University)"},"content":{"rendered":"<h4>Venue<\/h4>\n<p>Sala Seminari (Dip. Matematica).<\/p>\n<h4 class='mt-4'>Abstract<\/h4>\n<p>The nonlinear matrix equation X^p = A + M^T (X # B)M is considered, where p \u2265 1 is a positive integer, M is an n \u00d7 n nonsingular matrix, A is a positive semidefinite matrix and B is a positive definite matrix. We call C # D the geometric mean of positive definite matrices C and D. Some properties of the positive definite solution of the nonlinear matrix equation is investigated, including the existence and uniqueness of the solution, a lower and an upper bound. Iteration method for finding the numerical solution is proposed. Perturbation bounds with respect to small perturbations on the coefficient matrices are obtained. <\/p>\n","protected":false},"excerpt":{"rendered":"<p>The nonlinear matrix equation X^p = A + M^T (X # B)M is considered, where p \u2265 1 is a positive integer, M is an n \u00d7 n nonsingular matrix, A is a positive semidefinite matrix and B is a positive definite matrix. We call C # D the geometric mean of&hellip;<\/p>\n<p><a class=\"btn btn-dark btn-sm unipi-read-more-link\" href=\"https:\/\/www.dm.unipi.it\/en\/eventi\/on-the-positive-definite-solution-of-the-nonlinear-matrix-equation-xpamtxbm-jie-meng-pusan-national-university\/\">Read More&#8230;<\/a><\/p>\n","protected":false},"author":6,"featured_media":0,"template":"","tags":[],"unipievents_taxonomy":[],"class_list":["post-4531","unipievents","type-unipievents","status-publish","hentry"],"acf":[],"unipievents_startdate":1542880800,"unipievents_enddate":1542884400,"unipievents_place":"Sala Seminari (Dip. Matematica).","unipievents_externalid":0,"jetpack_sharing_enabled":true,"publishpress_future_workflow_manual_trigger":{"enabledWorkflows":[]},"_links":{"self":[{"href":"https:\/\/www.dm.unipi.it\/en\/wp-json\/wp\/v2\/unipievents\/4531","targetHints":{"allow":["GET"]}}],"collection":[{"href":"https:\/\/www.dm.unipi.it\/en\/wp-json\/wp\/v2\/unipievents"}],"about":[{"href":"https:\/\/www.dm.unipi.it\/en\/wp-json\/wp\/v2\/types\/unipievents"}],"author":[{"embeddable":true,"href":"https:\/\/www.dm.unipi.it\/en\/wp-json\/wp\/v2\/users\/6"}],"version-history":[{"count":0,"href":"https:\/\/www.dm.unipi.it\/en\/wp-json\/wp\/v2\/unipievents\/4531\/revisions"}],"wp:attachment":[{"href":"https:\/\/www.dm.unipi.it\/en\/wp-json\/wp\/v2\/media?parent=4531"}],"wp:term":[{"taxonomy":"post_tag","embeddable":true,"href":"https:\/\/www.dm.unipi.it\/en\/wp-json\/wp\/v2\/tags?post=4531"},{"taxonomy":"unipievents_taxonomy","embeddable":true,"href":"https:\/\/www.dm.unipi.it\/en\/wp-json\/wp\/v2\/unipievents_taxonomy?post=4531"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}