Distribution theory and transform analysis: an introduction to generalized functions, with applications
Introductory steps for an indexing based HDMR algorithm: lumping HDMR
MAASE'08 Proceedings of the 1st WSEAS International Conference on Multivariate Analysis and its Application in Science and Engineering
A reverse technique for lumping high dimensional model representation method
WSEAS Transactions on Mathematics
A reverse technique for lumping high dimensional model representation method
MAASE'09 Proceedings of the 2nd WSEAS international conference on Multivariate analysis and its application in science and engineering
Dosage planning for type 2 diabetes mellitus patients using Indexing HDMR
Expert Systems with Applications: An International Journal
An approximation method to model multivariate interpolation problems: Indexing HDMR
Mathematical and Computer Modelling: An International Journal
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A multivariate function f(x1,..., xN) can be evaluated via interpolation if its values are given at a finite number nodes of a hyperprismatic grid in the space of independent variables x1, x2,..., xN. Interpolation is a way to characterize an infinite data structure (function) by a finite number of data approximately. Hence it leaves an infinite arbitrariness unless a mathematical structure with finite number of flexibilities is imposed for the unknown function. Imposed structure has finite dimensionality. When the dimensionality increases unboundedly, the complexities grow rapidly in the standard methods. The main purpose here is to partition the given multivariate data into a set of low-variate data by using high dimensional model representation (HDMR) and then, to interpolate each individual data in the set via Lagrange interpolation formula. As a result, computational complexity of the given problem and needed CPU time to obtain the results through a series of programs in computers decrease.