Polynomial Interpolation, Numerical Methods #8

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Angewandte Mathematik für Ingenieure

Published on Oct 5, 2024
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What is meant by polynomial interpolation and what does the Vandermonde matrix or the Vandermonde determinant have to do with polynomial interpolation? In engineering practice, one very often comes across the task of laying a curve that is as smooth as possible through a number of given points and that is as easy to handle analytically as possible. In other words, a curve that can be easily differentiated and integrated. In this video, physicist Dietmar Haase proves that exactly one polynomial of the nth degree can be laid through n+1 given support points. This method, which is also known as polynomial interpolation, when applied to a linear system of equations with n+1 equations and just as many unknowns, results in the Vandermonde matrix, named after the French chemist and mathematician Alexandre Theophile Vandermonde. It is proven that the Vandermonde determinant is not equal to zero, which shows that a solution exists for the linear system of equations. Website: https://www.ingmathe.de Youtube channel: / ingmathede Online calculator: https://www.wolframalpha.com/

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