Polynomial Interpolation with Newton Polynomials Part 1, Numerical Methods #10

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Angewandte Mathematik für Ingenieure

Published on Nov 2, 2024
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What are Newton polynomials and why are Newton polynomials preferred over Lagrange polynomials in practice for polynomial interpolation? In this video, physicist Dietmar Haase explains why the Newton representation using Newton's basis polynomials is preferred over the Lagrange representation using Lagrange's basis polynomials for polynomial interpolation. The main disadvantage of the Lagrange representation is that every Lagrange basis polynomial depends on all of the support points. This means that if another support point is to be added, for example to increase the accuracy of the interpolation, then all of the Lagrange basis polynomials have to be recalculated. The Newton representation of the interpolation polynomial does not have this disadvantage. This is because when additional new support points are added, the Newton representation of the old support points can continue to be used without restriction. Among other things, it is shown that by adding another support point, only one additional base polynomial needs to be recalculated and the old base polynomials remain valid. This is also the reason why, in practice, the Newtonian representation of the interpolation polynomial is almost always used for the interpolation of data. Website: https://www.ingmathe.de Youtube channel: / ingmathede Online calculator: https://www.wolframalpha.com/

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