Wegstein's Method @OscarVeliz

Uploaded October 2018 | Updated September 2026, 2 weeks ago

Wegstein Method for finding roots, accelerating fixed point iteration, and inducing convergence in fixed point iteration. Explained examples and discussion of order as well as how to compute q. Example code: github.com/osveliz/numerical-veliz

Chapters
0:00 Intro
0:22 Wegstein's Method Sources
0:52 Wegstein's Methodology
1:56 Wegstein's Method Examples
3:24 Computing q
4:55 Computing q example
5:24 Updating q
5:43 Updating q example
6:03 Computational Order
6:36 Oscar's Notes
7:13 Thank You

See Video Mistakes II: The Sequel youtu.be/YEUbzqkJBf0 for a small error and correction.

Suggestions for further watching:
Fixed Point Iteration: youtu.be/OLqdJMjzib8
Steffensen's Method with Aitken's Δ²: youtu.be/BTYTj0r5PZE
Fixed Point Iteration Q&A youtu.be/FyCviw2ZA2o

References:
Wegstein's original paper: dl.acm.org/citation.cfm?id=368871
Gutzler's thesis: https://ir.library.oregonstate.edu/downloads/2r36v1962

#WegsteinsMethod #NumericalAnalysis

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Generalized False Position & Alternative Secant Methods

$Bairstows Method Bairstows Method for finding the roots of polynomials including complex roots. Discussion of method derivation, relation to synthetic division of two variables, stopping condition, selection of initial values, fractals, and historical context. Submission for Summer of Math Exposition 2 contest by @3blue1brown. Example code hosted on GitHub https://github.com/osveliz/numerical-veliz Chapters: 00:00 Intro 00:36 Factoring with monomial 01:13 Factoring with quadratic 01:40 Synthetic Division 1 variable 02:16 Synthetic Division 2 variables 03:22 Solving for roots 03:50 Different u and v 04:24 Describing Notation 05:22 Solving Nonlinear System 07:01 Another Synthetic Division 07:45 Updating u & v 08:27 Bairstow Iteration Example 08:56 Bairstow Iteration Example 2 09:22 Note on Quadratic Equation 09:42 Bairstow Full Algorithm 10:51 Complex Roots Example 11:33 Bairstow Fractals 12:23 Picking u & v 12:46 Henrici Starting Values 13:08 Bairstows Original Problem 14:40 Oscars Notes 15:24 Outro Recommended Viewing: Horners Method https://youtu.be/zEvfkSuPqWk Graeffes Method https://youtu.be/92oh5gYUP7Y Generalized Newtons Method https://youtu.be/p0SBubUfwiI Reference links: Applied Aerodynamics by Bairstow https://books.google.com/books?id=GIUQAQAAMAAJ Elements of Numerical Analysis by Henrici https://archive.org/details/elements-of-numerical-analysis-by-peter-henrici A Modified Bairstow Method for Multiple Zeros of a Polynomial by F. M. Carrano https://doi.org/10.1090/S0025-5718-1973-0334492-5 Background music Drifting at 432 Hz by @UnicornHeads #SoME2 #NumericalAnalysis #BairstowsMethod$