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High dimensional model representation for piece-wise continuous function approximation. (English) Zbl 1155.65014
Summary: 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.

65D15 Algorithms for approximation of functions
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[1] Rabitz, Efficient input-output model representations, Computer Physics Communications 117 pp 11– (1999) · Zbl 1015.68219
[2] Rabitz, General foundations of high dimensional model representations, Journal of Mathematical Chemistry 25 pp 197– (1999) · Zbl 0957.93004
[3] Alis, Efficient implementation of high dimensional model representations, Journal of Mathematical Chemistry 29 (2) pp 127– (2001) · Zbl 1051.93502
[4] Li, High dimensional model representations, Journal of Physical Chemistry A 105 pp 7765– (2001)
[5] Li, High dimensional model representations generated from low dimensional data samples-I. mp-Cut-HDMR, Journal of Mathematical Chemistry 30 pp 1– (2001) · Zbl 1023.81521
[6] Wang, Fully equivalent operational models for atmospheric chemical kinetics within global chemistry-transport models, Journal of Geophysical Research 104 (D23) pp 30417– (1999)
[7] Li, Global uncertainty assessments by high dimensional model representations (HDMR), Chemical Engineering Science 57 (21) pp 4445– (2002)
[8] Sobol, Theorems and examples on high dimensional model representations, Reliability Engineering and System Safety 79 pp 187– (2003)
[9] Balakrishnan, A comparative assessment of efficient uncertainty analysis techniques for environmental fate and transport models: application to the FACT model, Journal of Hydrology 307 (1-4) pp 204– (2005)
[10] Lancaster, Curve and Surface Fitting: an Introduction (1986) · Zbl 0649.65012
[11] Singh, A numerical solution of composite heat transfer problems using meshless method, International Journal of Heat and Mass Transfer 47 pp 2123– (2004) · Zbl 1050.80006
[12] Rao, An efficient meshless method for fracture analysis of cracks, Computational Mechanics 26 pp 398– (2000) · Zbl 0986.74078
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