Polynomial interpolation with Newton polynomials Part 2, Numerical Methods #11

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Angewandte Mathematik für Ingenieure

Published on Nov 9, 2024
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What do the divided differences have to do with polynomial interpolation using Newton's basic polynomials and how can the divided differences be easily determined using the Newton scheme? In this video, physicist Dietmar Haase shows how an interpolation polynomial can be set up using given support points in the Newton representation. It is shown that the coefficients of the interpolation polynomial in the Newton representation can be determined immediately and successively by inserting the support points, but that this naive approach results in an unnecessary number of arithmetic operations. However, the number of arithmetic operations can be significantly reduced by introducing so-called divided differences. It is also explained how the divided differences can be calculated recursively in a very simple and clear manner using the Newton scheme. Website: https://www.ingmathe.de Youtube channel: / ingmathede Online calculator: https://www.wolframalpha.com/

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