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High-dimensional model representation - Wikipedia, the free encyclopedia

High-dimensional model representation

From Wikipedia, the free encyclopedia

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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 that is used to determine the right hand side functions are given in Sobol's paper.

[edit] References

  • I. M. Sobol, Sensitivity estimates for nonlinear mathematical models, Mathematical Modeling and Computational Experiments, VOL. 1, 407-414, (1993)


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