High dimensional model representation for piece-wise continuous function approximation.

*(English)*Zbl 1155.65014Summary: High dimensional model representation (HDMR) approximates multivariate functions in such a way that the component functions of the approximation are ordered starting from a constant and gradually approaching to multivariance as we proceed along the terms like first-order, second-order and so on. Until now HDMR applications include construction of a computational model directly from laboratory/field data, creating an efficient fully equivalent operational model to replace an existing time-consuming mathematical model, identification of key model variables, global uncertainty assessments, efficient quantitative risk assessments, etc.

In this paper, the potential of HDMR for tackling univariate and multivariate piece-wise continuous functions is explored. Eight numerical examples are presented to illustrate the performance of HDMR for approximating a univariate or a multivariate piece-wise continuous function with an equivalent continuous function.

In this paper, the potential of HDMR for tackling univariate and multivariate piece-wise continuous functions is explored. Eight numerical examples are presented to illustrate the performance of HDMR for approximating a univariate or a multivariate piece-wise continuous function with an equivalent continuous function.

##### MSC:

65D15 | Algorithms for approximation of functions |

##### Keywords:

high dimensional model representation; univariate; multivariate; piece-wise continuous; function approximation; numerical examples
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\textit{R. Chowdhury} et al., Commun. Numer. Methods Eng. 24, No. 12, 1587--1609 (2008; Zbl 1155.65014)

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