Asymptotically Function Flattening Transformations via Taylor Polynomial and Affine Superoperator over Function Operators

Demiralp M.

International Conference on Numerical Analysis and Applied Mathematics (ICNAAM), Halkidiki, Greece, 19 - 25 September 2011, vol.1389 identifier identifier

  • Publication Type: Conference Paper / Full Text
  • Volume: 1389
  • Doi Number: 10.1063/1.3637830
  • City: Halkidiki
  • Country: Greece
  • Istanbul Technical University Affiliated: No


This work aims at the flattening of the functions. We first focus on the flattening of univariate functions, then what we obtain for the univariate functions are extended to the multivariate functions by following the tricky way used for the extension of univariate Taylor expansions to the multivariate functions. The flattening is basically accomplished by using univariate and multivariate Taylor expansions although some other expansions can also be used. Certain binary superoperators transforming the target function and independent variable(s) operators to another function operator of same type but with more asymptotic flatness are employed as auxiliary agents. The analyticity is assumed for both the operand function of the transformation and its image. The utilization of this method in combination with the numerical integration and high dimensional model representation (HDMR) will facilitate the numerical quality increase.