Oscar Veliz | Aberth-Ehrlich Method @OscarVeliz | Uploaded 5 years ago | Updated 1 hour ago
The Aberth-Ehrlich Method for solving all roots of a polynomial simultaneously including history, methodology, examples, and order as well as comparison to Durand-Kerner. Example code github: http://github.com/osveliz/numerical-veliz

Chapters
0:00 Intro
0:19 History
0:41 Methodology
0:59 Starting Points
1:11 Starting Points Visualized
1:33 Newton Fractal
2:22 A Modified Newton Method
2:35 Ehrlich's Derivation
4:43 Example
5:09 Durand-Kerner versus Aberth-Ehrlich
6:22 Behavior of Aberth-Ehrlich
6:33 Notes on Aberth-Ehrlich
7:01 Thank You

Further viewing:
Durand-Kerner youtu.be/5JcpOj2KtWc
Laguerre's Method youtu.be/blOARV4lnIM
Newton Fractals youtu.be/MWD2A0Vg2V0
Bairstow's Method youtu.be/iUGEk6kngFw

References:
Aberth's paper ams.org/journals/mcom/1973-27-122/S0025-5718-1973-0329236-7
Ehrlich's paper dl.acm.org/citation.cfm?id=363115
Kerner link.springer.com/article/10.1007%2FBF02162564
Algorithm 283 dl.acm.org/citation.cfm?id=365527
Wilkinson dl.acm.org/citation.cfm?id=1096474
Maehly link.springer.com/article/10.1007/BF01600333
Börsch link.springer.com/article/10.1007%2FBF01385904

#DurandKerner #AberthEhrlich #NumericalAnalysis