The influence of the support functions on the quality of enhanced multivariance product representation
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This paper presents recently developed Enhanced Multivariance Product Representation (EMPR) method for multivariate functions. EMPR disintegrates a multivariate function to components which are respectively constant, univariate, bivariate and so on in ascending multivariance. Although the EMPR method has the same philosophy with the High Dimensional Model Representation (HDMR) method, it has been proposed to get better quality than HDMR’s with the help of the support functions. For this purpose, we investigate the EMPR truncation qualities with respect to the selection of the support functions. The obtained results and a number of numerical implementations to show the efficiency of the method are also given in this paper.
KeywordsHigh dimensional model representation Multivariate functions Approximation
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- 1.I.M. Sobol, Sensitivity estimates for nonlinear mathematical models. Math. Model. Comput. Exp. (MMCE) 1, No. 4.407 (1993)Google Scholar
- 4.Li G., Rosenthal C., Rabitz H.: High dimensional model representations. J. Math. Chem. A 105, 7765–7777 (2001)Google Scholar
- 5.M. Demiralp, M.A. Tunga, High dimensional model representation of multivariate interpolation via hypergrids. The Sixteenth international symposium on computer and information sciences (ISCIS XVI), pp. 416–423 (2001)Google Scholar
- 6.Demiralp M.: High dimensional model representations and its application varieties. Mathe. Res. 9, 146–159 (2003)Google Scholar
- 7.M.A. Tunga, M. Demiralp, Bound analysis in univariately truncated generalized high dimensional model representation for random-data partitioning: interval GHDMR. App. Numer. Math. (2008). doi: 10.1016/j.apnum.2008.06.006
- 8.M.A. Tunga, M. Demiralp, Computational complexity investigations for high dimensional model representation algorithms Used in multivariate interpolation problems, 12th WSEAS international conference on applied mathematics, pp. 133–139, Dec 29–31, Cairo, Egypt (2007)Google Scholar
- 11.B. Tunga, M. Demiralp, Support function influences on the univariance of the enhanced multivariance product representation, Seventh International Conference of Computational Methods in Sciences and Engineering (Rhodes, Greece, 2009)Google Scholar
- 12.M. Demiralp, Important aspects of enhanced multivariance product representation, (to be published)Google Scholar
- 13.Oevel W., Postel F., Wehmeier S., Gerhard J.: The MuPAD Tutorial. Springer, Berlin (2000)Google Scholar