{"42810":{"#nid":"42810","#data":{"type":"event","title":"Computing the joint spectral radius for some of nonnegative matrices","body":[{"value":"\u003Cp\u003E\u003Cstrong\u003ETITLE:\u003C\/strong\u003E Computing the joint spectral radius for some sets of nonnegative matrices \n\u003C\/p\u003E\n\u003Cp\u003E\u003Cstrong\u003ESPEAKER:\u003C\/strong\u003E Dr. Yuri Nesterov\n\u003C\/p\u003E\n\u003Cp\u003E\u003Cstrong\u003EABSTRACT:\u003C\/strong\u003E\n\u003C\/p\u003E\n\u003Cp\u003EWe propose two simple upper bounds for the Joint Spectral Radius (JSR) of arbitrary sets of nonnegative matrices. These bounds, the Joint Column Radius, and the Joint Row Radius, can be computed in polynomial time as solutions to some convex optimization problems. We show that for general matrices they are within a factor ${1 over n}$ of the exact value, where $n$ is the size of the matrices. However, for the set of matrices with independent column (or row) uncertainties, the corresponding bounds coincide with JSR. As a byproduct of this result, we get a possibility to solve in polynomial time some boolean optimization problems related to spectral radius. We present also other economical and engineering applications of our results, which were never considered in computational practice in view of their intrinsic complexity. \u003C\/p\u003E","summary":null,"format":"limited_html"}],"field_subtitle":"","field_summary":[{"value":"Computing the joint spectral radius for some sets of nonnegative matrices","format":"limited_html"}],"field_summary_sentence":[{"value":"Computing the joint spectral radius for some of nonnegative matrices"}],"uid":"27187","created_gmt":"2009-10-12 20:36:08","changed_gmt":"2016-10-08 01:47:09","author":"Anita Race","boilerplate_text":"","field_publication":"","field_article_url":"","field_event_time":{"event_time_start":"2009-04-03T12:00:00-04:00","event_time_end":"2009-04-03T13:00:00-04:00","event_time_end_last":"2009-04-03T13:00:00-04:00","gmt_time_start":"2009-04-03 16:00:00","gmt_time_end":"2009-04-03 17:00:00","gmt_time_end_last":"2009-04-03 17:00:00","rrule":null,"timezone":"America\/New_York"},"extras":[],"groups":[{"id":"1242","name":"School of Industrial and Systems Engineering (ISYE)"}],"categories":[],"keywords":[{"id":"5303","name":"matrices"}],"core_research_areas":[],"news_room_topics":[],"event_categories":[{"id":"1795","name":"Seminar\/Lecture\/Colloquium"}],"invited_audience":[],"affiliations":[],"classification":[],"areas_of_expertise":[],"news_and_recent_appearances":[],"phone":[],"contact":[{"value":"\u003Cstrong\u003EAnita  Race\u003C\/strong\u003E\u003Cbr \/\u003EH. Milton Stewart School of Industrial and Systems Engineering\u003Cbr \/\u003E\u003Ca href=\u0022http:\/\/www.gatech.edu\/contact\/index.html?id=ar9\u0022\u003EContact Anita  Race\u003C\/a\u003E","format":"limited_html"}],"email":[],"slides":[],"orientation":[],"userdata":""}}}