Error propagation through generalized high dimensional model representation for data partitioning

Abstract

In many circumstances the explicit form of a multivariate function is not known; rather a finite number of data is listed from some physical experiments. In such cases a function can be constructed only by imposing some analytical structures containing a finite number of adjustable parameters to fit the function with the given values at some specified points. This means interpolation. The given data is collected or produced by some devices or means which may cause unavoidable errors. This results in an uncertainty band for each datum. The propagation of these errors through the interpolation is the focus of this work. It uses a new form of a partitioning technique called Generalized High Dimensional Model Representation (GHDMR). GHDMR is a divide-and-conquer approach starting from a constant component and proceeding upto high variate terms, univariate, bivariate and so on in the representation. The representation is truncated by keeping only constant and univariate terms for approximation. In other words just a single N variate problem is approximated by N univariate problem.