Halley's Method

Описание: 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