General Mathematics

   

Improved Interpolation and Approximation Through Order Manipulation

Authors: Vahid Rahmati

A novel transform calling smoothing, which can improve interpolation and reduce approximation error, is introduced in this paper. This method can be applied to various formulas, including interpolation and approximation methods, which are denoted in the process of order manipulation. Subsequently, the paper shows how to achieve higher degree polynomial approximations through fewer interpolation points, which is impossible with ordinary methods of interpolation. In fact, this leads to an alternative solution to oscillatory behavior and Runge’s phenomenon occurring in polynomial interpolations or methods of least squares approximation when the number of points is increased significantly to achieve higher degree polynomials with the aim of error reduction. Several ideas—in the form of theorems and their proofs—are therefore studied on the basis of smoothing process of the interpolation. Finally, a comprehensive comparison, with the intention of showing the advantage of the new transform over other methods in the form of MSE v. number of samples, is provided.

Comments: 10 Pages.

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Submission history

[v1] 2017-11-22 02:45:39

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