Plenary Lecture
On the Transformational HDMR Method
Professor N. A. Baykara
Marmara University
Mathematics Department
Istanbul, TURKEY
E-mail: nabaykara@gmail.com
Abstract: High Dimensional Model Representation Method (HDMR) is a divide and con quer technique originally suggested by I.M. Sobol later developed by H. Rabitz and M. Demiralp. Various requirements urged these authors as well as others to develop different versions of HDMR. Some of these like Cut HDMR, Mul ticut HDMR, Random Sampling HDMR etc. were suggested for tackling with large numbers of data processing. Such HDMR versions however, will be out of the scope of this talk. An alternative route was dealing with functions of multiplicative nature rather than of additive nature. To this end Demiralp's group developed HDMR versions like Factorized HDMR, Hybrid HDMR and Logarithmic HDMR. The last of these, is based on the idea of transforming a function of multiplicative nature to one of additive nature simply by taking its logarithm. Applying the standard (i.e. Plain) HDMR to this newly obtained function, HDMR components are obtained. This is followed by exponentia tion of HDMR components. It was the fundamental idea behind Logarithmic HDMR which led to the possibility of using alternative transformations and inverse transformations. As a result the more general idea of Transformational HDMR was suggested again by the Demiralp group. Transformational HDMR has been used to develop new approximations of various functions. To this end Rational as well as Conical and Mobius Transformations were used. The major issue to be discussed will be these recently developed approximation techniques which are believed to give good alternatives, to say the least, to approximation methods like Pade or Hermite-Pade.
Brief Biography of the Speaker: N. A. BAYKARA was born in Istanbul,Turkey on 29th July 1948. He received a B.Sc. degree in Chemistry from Bosphorous University in 1972. He obtained his PhD from Salford University, Greater Manchester, Lancashire,U.K. in 1977 with a thesis entitled “Studies in Self Consistent Field Molecular Orbital Theory”, Between the years 1977–1981 and 1985–1990 he worked as a research scientist in the Applied Maths Department of The Scientific Research Council of Turkey. During the years 1981-1985 he did postdoctoral research in the Chemistry Department of Montreal University, Quebec, Canada. Since 1990 he is employed as a Staff member of Marmara University. He is now a Full Professor of Applied Mathematics mainly teaching Numerical Analysis courses and is involved in HDMR research and is a member of Group for Science and Methods of Computing in Informatics Institute of Istanbul Technical University. Other research interests of his for him are “Density Functional Theory” and “Fluctuationlessness Theorem and its Applications” which he is actually involved in. Most recent of his concerns is focused at efficient remainder calculations of Taylor expansion via Fluctuation–Free Integration, and Fluctuation–Free Expectation Value Dynamics.