An Integration Free Universal Approximation Method Based on Orthogonal Polynomials

Yaman I., Demiralp M.

International Conference on Numerical Analysis and Applied Mathematics, Psalidi, Greece, 16 - 20 September 2008, vol.1048, pp.601-604 identifier

  • Publication Type: Conference Paper / Full Text
  • Volume: 1048
  • City: Psalidi
  • Country: Greece
  • Page Numbers: pp.601-604


In this work, we focus on the development of a novel polynomial approximation method, which is based on orthogonal expansion. Although the basis set elements of the expansion will be chosen polynomials or multinomials to this end, the method is open to any kind of complete set of basis functions. The projection integrals are replaced with certain quadratic forms over the matrix representation of the independent variable. This brings the universality and reduces the computational complexity drastically. Hence, it can be conjectured that this method. will find quite large area of applicability. Another advantage of this technique is, that it is not limited to univariate cases, and can be used for the multivariate cases by taking necessary precautions to get efficiency