Hybrid high dimensional model representation (HHDMR) on the partitioned data
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Dosyalar
Tarih
2006-01-01
Yazarlar
Dergi Başlığı
Dergi ISSN
Cilt Başlığı
Yayıncı
Elsevier B.V.
Erişim Hakkı
info:eu-repo/semantics/closedAccess
Özet
A multivariate interpolation problem is generally constructed for appropriate determination of a multivariate function whose values are given at a finite number of nodes of a multivariate grid. One way to construct the solution of this problem is to partition the given multivariate data into low-variate data. High dimensional model representation (HDMR) and generalized high dimensional model representation (GHDMR) methods are used to make this partitioning. Using the components of the HDMR or the GHDMR expansions the multivariate data can be partitioned. When a cartesian product set in the space of the independent variables is given, the HDMR expansion is used. On the other band, if the nodes are the elements of a random discrete data the GHDMR expansion is used instead of HDMR. These two expansions work well for the multivariate data that have the additive nature. If the data have multiplicative nature then factorized high dimensional model representation (FHDMR) is used. But in most cases the nature of the given multivariate data and the sought multivariate function have neither additive nor multiplicative nature. They have a hybrid nature. So, a new method is developed to obtain better results and it is called hybrid high dimensional model representation (HHDMR). This new expansion includes both the HDMR (or GHDMR) and the FHDMR expansions through a hybridity parameter. In this work, the general structure of this hybrid expansion is given. It has tried to obtain the best value for the hybridity parameter. According to this value the analytical structure of the sought multivariate function can be determined via HHDMR.
Açıklama
Anahtar Kelimeler
High dimensional model representation, Factorized high dimensional model representation, Multivariate functions, Interpolation, Multidimensional problems, Approximation, Optimization, Approximation theory, Data reduction, Functions, Mathematical models, Factorized high dimensional model representation (FHDMR), Hybrid high dimensional model representation (HHDMR), Multivariable systems
Kaynak
Journal of Computational and Applied Mathematics
WoS Q Değeri
Q1
Scopus Q Değeri
Q2
Cilt
185
Sayı
1
Künye
Tunga, M. A. & Demiralp, M. (2006). Hybrid high dimensional model representation (HHDMR) on the partitioned data. Journal of Computational and Applied Mathematics, 185(1), 107-132. doi:10.1016/j.cam.2005.01.030
