Newton's method (Newton-Raphson method), Classical Algebra #42

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Angewandte Mathematik für Ingenieure

Published on Jun 29, 2024
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What is Newton's method or what is the Newton-Raphson method and how can the Newton method be used to approximately determine the zeros of a real function with one variable numerically? In this video, physicist Dietmar Haase shows how the zeros of a real nonlinear function with one real variable can be found numerically using Newton's method. Newton's method is generally used to solve equations that cannot be solved algebraically or can only be solved with considerable computational effort. The advantages of Newton's method are essentially the rapid convergence of the iteration, provided that the starting value of the iteration lies in the catchment area of ​​the zero being sought. A selected example shows how a real zero for a quintic equation can be approximately calculated using Newton's method. In contrast to the bisection method and the secant method, Newton's method also requires that the function under consideration must be differentiable with a derivative other than zero. The disadvantages of Newton's method are that if you choose a starting value that is not in the catchment area of ​​the zero point you are looking for, there is no guarantee that Newton's method will converge to the zero point you are looking for. Website: https://www.ingmathe.de Youtube channel: / ingmathede Online calculator: https://www.wolframalpha.com/

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