High-dimensional model representation

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High-dimensional model representation is a finite expansion for a given multivariable function. The expansion is first described by Sobol' as

$f(\mathbf{x}) = f_0+ \sum_{i=1}^nf_i(x_i)+ \sum_{i,j=1 \atop i<j}^n f_{ij}(x_{j},x_{j})+ \cdots + f_{12\ldots n}(x_1,\ldots,x_n).$

The method, used to determine the right hand side functions, is given in Sobol's paper.

[edit] References

I. M. Sobol', Sensitivity estimates for nonlinear mathematical models, Mathematical Modeling and Computational Experiments, v. 1, 407-414, (1993)
High Dimensional Model Representation (HDMR): Concepts and Applications