Plenary Lecture

EHDMR Based Bound Analysis Methods in Multivariate Interpolation Problems

Assistant Professor M. Alper Tunga
Bahcesehir University
Software Engineering Department
Istanbul, Turkey
E-mail: alper.tunga@bahcesehir.edu.tr

Abstract: If a multivariate data set is given to specify a multivariate function and it is asked to determine an analytical structure for the sought multivariate function, instead of using standard interpolation methods, given multivariate data can be partitioned into low–variate data and then an analytical structure is determined with the aid of these partitioned data.
However, the given data is collected or produced by some devices or means which may cause unavoidable errors. This results in an uncertainty interval for each datum. The errors in data may come from their construction because of the incapabilities or limited capabilities of the devices, tools, and/or algorithms used to construct data. This implies that each component of data is reliable only within an interval which contains the data value. If the length of the interval is assumed to be sufficiently small to enable us to approximate the differentiation operator with corresponding order difference operator then we may proceed to make an error analysis which reveals how the errors propagate.
The main purpose here is to determine the analytical structure of a multivariate function when a data set including measurement or construction errors is given. In this case, not a unique structure but a band structure with a presumably small thickness will be obtained for the multivariate function in accordance with the given data set and the given error ratios for this data set.
In this lecture, Interval GHDMR, Interval FHDMR and Interval HHDMR methods are given to explain one way of obtaining these abovementioned band structures for the given multivariate interpolation problems in which the errors in data occur.

Brief Biography of the Speaker:
M. Alper TUNGA was born in Istanbul, Turkey on 11th June 1975. He received a B.Sc. degree in Mathematics Engineering from ? Istanbul Technical University (I.T.U.) in 1997. He got his M.Sc. degree in Systems Analysis from Istanbul Technical University in 1999. He got a PhD from Istanbul Technical University in 2006 with a thesis entitled “Data Partitioning and Multivariate Interpolation via Various High Dimensional Model Representations ”. In 1998, he worked as a research assistant in Computational Science and Engineering Department of I.T.U. Between the years 1999-2006 he worked as a research assistant in the Computer Engineering Department of Isk University of Turkey. Since 2007, he is Assistant Professor in Bahcesehir University. He is also a member of Group for Science and Methods of Computing in Informatics Institute of Istanbul Technical University. He is working on methodology for computational sciences. His interests are HDMR, Multivariate Data Modelling and Data Mining. M. Alper Tunga has 7 papers about these subjects in various scientific journals.