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Halley's Method

Halley's Method (the method of tangent hyperbolas) for finding roots including history, derivation, examples, and fractals. Also discusses Taylor's Theorem relating to Halley's Method as well as Halley's Comet. Sample code and images available on GitHub https://www.github.com/osveliz/numeri... Chapters 00:00 Intro 00:36 History 03:48 Derivation Setup 05:20 Derivation Tangent Hyperbolas 06:00 Derivation Taylor Series 07:21 Example 07:53 Example 2 (see correction) 08:24 Newton versus Halley 08:45 Example 3 09:29 Halley Fractals 11:27 Summary 11:52 Thank You Corrections: The example at 8:08 had an error with the programming of f'(x). The bug caused the numbers in the table and the plots for that example to be incorrect. There is a separate issue in that example where 2 was written as the input instead of -2. Also there is typo in the name Christopher Wren at 0:46. A video covering these corrections can be found here    • Video Mistakes and How to Fix Them   Suggested viewing: Newton's Method    • Newton's Method   Newton Convergence Interval    • Newton's Method Interval of Convergence   Newton Fractal    • Newton Fractals   Laguerre's Method    • Laguerre's Method   Householder's Method    • Householder's Method   Reference Links: On the Geometry of Halley's Method - https://www.jstor.org/stable/2975033 Halley's Method (Latin) - https://royalsocietypublishing.org/do... Halley's Method (English) - https://biodiversitylibrary.org/page/... Thomas Fantet de Lagny (French) - https://nubis.univ-paris1.fr/ark%3A/1... Raphson's Book (Latin) - https://archive.org/details/bub_gb_4n... A Synopsis of the Astronomy of Comets (English) - https://library.si.edu/digital-librar... A Synopsis of the Astronomy of Comets (Latin) - https://www.jstor.org/stable/102980 Principia (English) - https://openlibrary.org/books/OL70890... Principia (Latin) - https://www.loc.gov/item/28020872 Brook Taylor and the Method of Increments - https://link.springer.com/article/10.... Royal Society Charter - http://ttp.royalsociety.org/ttp/ttp.h... Song: "A Quiet Thought" by Wayne Jones #HalleysMethod #NumericalAnalysis