Video Mistakes II: The Sequel @OscarVeliz

Uploaded November 2020 | Updated September 2026, 2 weeks ago

This video corrects mistakes in my videos on Taylor Series Origin, Ternary Search, Dichotomous Search, Fixed Point Iteration for Fixed Point Iteration System of Equations with Banach, and Wegstein's Method. Thanks to commenters who pointed these errors out. If you find other mistakes feel free to comment or post in the GitHub Issues Forum for the code repository github.com/osveliz/numerical-veliz

Chapters
0:00 Intro
0:11 Taylor Series Origin youtu.be/KJYauVgXA4E
0:44 Ternary Search youtu.be/7h86n97naH4
0:54 Dichotomous Search youtu.be/n_zefNBfhSM
1:04 Fixed Point Iteration System of Equations with Banach youtu.be/xa2vUsYJD-c
1:19 Wegstein's Method youtu.be/T_6mR6rJXQQ
1:58 Outro

Check out the first episode of Video Mistakes: youtu.be/4jw0cjddmB8

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

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