Graeffe's Method

Graeffe's Root-Squaring Method (also called Graeffe-Dandelin-Lobachevskiĭ or Dandelin–Lobachesky–Graeffe method) for finding roots of polynomials. The method solves for all of the roots of a polynomial by only using the coefficients and does not require derivatives nor an interation function. This lesson provides a history of the method, motivates "why" the method works, and walks through an example of root-squaring as well as solving for the roots using logarithms. Example code hosted on GitHub https://github.com/osveliz/numerical-veliz Chapters: 00:00 Intro 00:45 History 01:10 Expanding & Reversing 02:21 Bracket Notation 03:53 Bracket Example 04:16 Solving for a 05:46 Solving for b 06:11 Solving for c 06:30 How does this help??? 06:55 Root Squaring Example 07:56 Repeated Root Squaring 08:36 Stopping Criteria 08:58 On Programming Graeffe's Method 09:30 Further Reading 09:52 Oscar's Notes 10:33 Outro Recommended Viewing: Horner's Method https://youtu.be/zEvfkSuPqWk Bairstow's Method https://youtu.be/iUGEk6kngFw Durand-Kerner https://youtu.be/5JcpOj2KtWc Aberth-Ehrlich https://youtu.be/XIzCzfMDSzk Reference links: Graeffe's Version https://publikationsserver.tu-braunschweig.de/receive/dbbs_mods_00051359 Dandelin's Version https://eudml.org/doc/180464 Lobachevskiĭ's Version https://catalog.lindahall.org/permalink/01LINDAHALL_INST/19lda7s/alma999251234705961 Householder's Article https://doi.org/10.2307/2310626 Brodetsky and Smeal 1924 https://doi.org/10.1017/S0305004100002802 Whittaker and Robinson https://books.google.com/books?id=0mUGAQAAIAAJ&ots=lFy0VTVeAd&dq=Whittaker%2C%20Edmund%20Taylor%2C%20and%20George%20Robinson.%C2%A0The%20calculus%20of%20observations%3A%20a%20treatise%20on%20numerical%20mathematics.%20Blackie%2C%201924.&lr&pg=PR3#v=onepage&q&f=false Best's Paper https://doi.org/10.2307/2306166 Background music "Drifting at 432 Hz" by @UnicornHeads #NumericalAnalysis #rootfinding #polynomials