{"55398":{"#nid":"55398","#data":{"type":"event","title":"Residual Updating Algorithms for Kernel Interpolation","body":[{"value":"\u003Cp\u003E\u003Cstrong\u003ETITLE:\u003C\/strong\u003E Residual Updating Algorithms for Kernel Interpolation\u003C\/p\u003E\u003Cp\u003E\u003Cstrong\u003ESPEAKER:\u003C\/strong\u003E Greg Fasshauer\u003C\/p\u003E\u003Cp\u003E\u003Cstrong\u003EABSTRACT:\u003C\/strong\u003E\u003C\/p\u003E\u003Cp\u003EI will first present two scattered data approximation methods \nfrom a numerical analysis point of view: radial basis function or kernel \ninterpolation and moving least squares approximation. Then I will \nintroduce the idea of approximate moving least squares approximation and \nconnect all three methods via a residual updating algorithm. In parallel \nI will attempt to point out connections to an analogous set of methods \n(kriging, local polynomial regression and higher-order kernels for \ndensity estimation) in statistics. The idea of residual updating will be \nilluminated both from a more analytical perspective and at the numerical \nlinear algebra level where we have rediscovered an old algorithm due to \nRiley [1].\n\u003Cbr \/\u003E[1] J.D. Riley. Solving systems of linear equations with a positive \ndefinite, symmetric, but possibly ill-conditioned matrix. Mathematical \nTables and Other Aids to Computation 9\/51 (1955), 96\u2013101.\n\u003Cbr \/\u003E\n\u003Cbr \/\u003EBrief bio:\n\u003Cbr \/\u003EGreg Fasshauer\n\u003Cbr \/\u003EProfessor, Associate Chair and Director of Undergraduate Studies\n\u003Cbr \/\u003EIllinois Institute of Technology\n\u003Cbr \/\u003EDepartment of Applied Mathematics\n\u003Cbr \/\u003EChicago, IL 60616\n\u003Cbr \/\u003E\n\u003Cbr \/\u003EEducation and Positions\n\u003Cbr \/\u003E* Since 1997: Assistant, associate and full professor, Department of \nApplied Mathematics, IIT\n\u003Cbr \/\u003E* Ralph P. Boas Visiting Assistant Professor: Department of Mathematics, \nNorthwestern University (1995-1997)\n\u003Cbr \/\u003E* Ph.D. (Mathematics): Vanderbilt University with Larry L. Schumaker (1995)\n\u003Cbr \/\u003E* M.A. (Mathematics): Vanderbilt University with Larry L. Schumaker (1993)\n\u003Cbr \/\u003E* Diplom (Mathematics) \u0026amp; Staatsexamen (Mathematics and English): \nUniversity of Stuttgart with Klaus H\u00f6llig (1991)\n\u003Cbr \/\u003E\n\u003Cbr \/\u003EResearch Interests (currently supported by NSF)\n\u003Cbr \/\u003E* Meshfree approximation methods for multivariate approximation and \ntheir application\n\u003Cbr \/\u003E* Radial basis functions and positive definite kernels\n\u003Cbr \/\u003E* Approximation theory\n\u003Cbr \/\u003E* Computer-aided geometric design\n\u003Cbr \/\u003E* Spline theory\n\u003Cbr \/\u003E* Numerical solution of PDEs\n\u003Cbr \/\u003E\n\u003Cbr \/\u003EBooks and 40+ papers\n\u003Cbr \/\u003E* Meshfree Approximation Methods with MATLAB\n\u003Cbr \/\u003EInterdisciplinary Mathematical Sciences - Vol. 6 World Scientific \nPublishers, Singapore, 2007\n\u003Cbr \/\u003E* Progress on Meshless Methods (edited with A.J.M. Ferreira, E.J. Kansa, \nand V.M.A. Leit\u00e3o)\n\u003Cbr \/\u003EComputational Methods in Applied Sciences, Vol. 11 Springer, Berlin, 2009\u003C\/p\u003E","summary":null,"format":"limited_html"}],"field_subtitle":"","field_summary":[{"value":"\u003Cp\u003EResidual Updating Algorithms for Kernel Interpolation\u003C\/p\u003E","format":"limited_html"}],"field_summary_sentence":[{"value":"Residual Updating Algorithms for Kernel Interpolation"}],"uid":"27187","created_gmt":"2010-04-19 07:47:05","changed_gmt":"2016-10-08 01:51:18","author":"Anita Race","boilerplate_text":"","field_publication":"","field_article_url":"","field_event_time":{"event_time_start":"2010-04-21T11:00:00-04:00","event_time_end":"2010-04-21T12:00:00-04:00","event_time_end_last":"2010-04-21T12:00:00-04:00","gmt_time_start":"2010-04-21 15:00:00","gmt_time_end":"2010-04-21 16:00:00","gmt_time_end_last":"2010-04-21 16:00:00","rrule":null,"timezone":"America\/New_York"},"extras":[],"groups":[{"id":"1242","name":"School of Industrial and Systems Engineering (ISYE)"}],"categories":[],"keywords":[],"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":[],"email":[],"slides":[],"orientation":[],"userdata":""}}}