Lecture Notes in Numerical Analysis with Mathematica

Lecture Notes in Numerical Analysis with Mathematica

Indexed in: EBSCO.

“ Lecture Notes in Numerical Analysis with Mathematica” highlights most of the important algorithms and their solved examples by Mathematica. The contents of this book include chapters on ...
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Natural and Generalized Interpolating Polynomials

Pp. 27-62 (36)

Krystyna STYš and Tadeusz STYš

Abstract

In this chapter, Lagranges and Hermits interpolation by polynomials, by trigonometric polynomials, by Chebyshevs polynomials and by generalized polynomials spanned on Chebyshevs systems of coordinates are presented. Lagranges and Newtons formulas to find the interpolating polynomials are derived and clarified. Mathematica modules are designed to determine interpolating polynomials. Fundamental theorems on interpolation with the errors bounds are stated and proved. The application of the theorems has been elucidated by examples. The Chapter ends with a set of questions.

Keywords:

Lagrange polynomials, Newton polynomials, Chebyshev polynomials.

Affiliation:

University of Warsaw, Poland.