{"44583":{"#nid":"44583","#data":{"type":"event","title":"ISyE Guest Lecturer:  Joel A. Tropp","body":[{"value":"\u003Cp\u003E\u003Cstrong\u003ESparse Solutions to Underdetermined Linear Systems\u003C\/strong\u003E\n\u003C\/p\u003E\n\u003Cp\u003E\u003Cstrong\u003EGUEST LECTURER\u003C\/strong\u003E\u003Cbr \/\u003E\nJoel A. Tropp\n\u003C\/p\u003E\n\u003Cp\u003E\u003Cstrong\u003EAFFILIATION\u003C\/strong\u003E\u003Cbr \/\u003E\nThe University of Michigan\n\u003C\/p\u003E\n\u003Cp\u003E\u003Cstrong\u003EABSTRACT\u003C\/strong\u003E\u003Cbr \/\u003E\nA fundamental problem in applied mathematics, statistics, and electrical engineering is to solve underdetermined systems of linear equations. Basic linear algebra seems to forbid this possibility. But a recent strand of research has established that certain underdetermined systems can be solved robustly with efficient algorithms, provided that the solution is sparse (i.e., has many zero components). This talk provides an overview of these sparse representation problems, and it describes the basic algorithmic approaches. Then it details situations where the algorithms are guaranteed to succeed. In particular, the talk introduces some new work on the case where the matrix is deterministic and the sparsity pattern is random. It also covers some results for the case where the matrix is random, which is the situation in Compressed Sensing applications.\n\u003C\/p\u003E","summary":null,"format":"limited_html"}],"field_subtitle":"","field_summary":[{"value":"Sparse Solutions to Underdetermined Linear Systems.","format":"limited_html"}],"field_summary_sentence":[{"value":"ISyE Guest Lecturer:  Joel A. Tropp"}],"uid":"27216","created_gmt":"2009-10-12 21:22:56","changed_gmt":"2016-10-08 01:48:27","author":"Ruth Gregory","boilerplate_text":"","field_publication":"","field_article_url":"","field_event_time":{"event_time_start":"2007-01-25T10:00:00-05:00","event_time_end":"2007-01-25T11:00:00-05:00","event_time_end_last":"2007-01-25T11:00:00-05:00","gmt_time_start":"2007-01-25 15:00:00","gmt_time_end":"2007-01-25 16:00:00","gmt_time_end_last":"2007-01-25 16:00:00","rrule":null,"timezone":"America\/New_York"},"extras":[],"groups":[{"id":"1242","name":"School of Industrial and Systems Engineering (ISYE)"}],"categories":[],"keywords":[{"id":"6393","name":"ISyE Guest Lecturer"},{"id":"6414","name":"Joel A. Tropp"}],"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\u003EXiaoming Huo\u003C\/strong\u003E\u003Cbr \/\u003EISyE\u003Cbr \/\u003E\u003Ca href=\u0022mailto:xiaoming.huo@isye.gatech.edu\u0022\u003EContact Xiaoming Huo\u003C\/a\u003E\u003Cbr \/\u003E\u003Cstrong\u003E404-894-2300\u003C\/strong\u003E","format":"limited_html"}],"email":[],"slides":[],"orientation":[],"userdata":""}}}