Multi Nodalset Fluctuation Free Approximation in Taylor Remainder's Evaluation

Abstract

The matrix representation of a univariate function is equal to the image of the independent variable matrix representation under that function at the no fluctuation limit. In recent studies this fact is extended in such a way that the matrix representation of a univariate function can be expressed as a linear combination of the same function with two different matrix arguments. This idea makes us think for more than two matrices whose images under the target function are combined to get better approximation. This paper focuses on the application of this approximation method on the integral representation of the remainder term of the Taylor series expansion. In this work the basic conceptual background is given. Some illustrative implementations will be given at the relevant conference presentation.