MATH'07 Proceedings of the 12th WSEAS International Conference on Applied Mathematics
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High Dimensional Model Representation (HDMR) is constructed to basically use product type weight functions. This is because of the vanishing integral (for Continuous HDMR) or sum (for Discrete HDMR) impositions. If an HDMR based on nonproduct type weight functions is desired to be constructed then it is quite natural to attempt changing impositions. This can be realized in such a way that the nonproduct type weight is approximated as a product of univariate functions each of which is the average on all possible values of the all variables except a chosen one which is different for each factor. Then the deviation of the nonproduct type weight function from this product can be treated as perturbation and all components can be perturbatively determined. As a gentle introduction to the issue we focus on the HDMR for bivariate functions. However what we obtain seems to be extendable to the HDMR case of any multivariance.