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- W2130699922 abstract "Abstract The High Dimensional Model Representation (HDMR) technique is a procedure for efficiently representing high‐dimensional functions. A practical form of the technique, RS‐HDMR, is based on randomly sampling the overall function and utilizing orthonormal polynomial expansions. The determination of expansion coefficients employs Monte Carlo integration, which controls the accuracy of RS‐HDMR expansions. In this article, a correlation method is used to reduce the Monte Carlo integration error. The determination of the expansion coefficients becomes an iteration procedure, and the resultant RS‐HDMR expansion has much better accuracy than that achieved by direct Monte Carlo integration. For an illustration in four dimensions a few hundred random samples are sufficient to construct an RS‐HDMR expansion by the correlation method with an accuracy comparable to that obtained by direct Monte Carlo integration with thousands of samples. © 2003 Wiley Periodicals, Inc. J Comput Chem 24: 277–283, 2003" @default.
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- W2130699922 date "2003-01-09" @default.
- W2130699922 modified "2023-09-29" @default.
- W2130699922 title "Correlation method for variance reduction of Monte Carlo integration in RS-HDMR" @default.
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- W2130699922 doi "https://doi.org/10.1002/jcc.10172" @default.
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