Uploaded August 2022 | Updated September 2026, 2 weeks ago
Bairstow's 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 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 Bairstow's Original Problem
14:40 Oscar's Notes
15:24 Outro
Recommended Viewing:
Horner's Method youtu.be/zEvfkSuPqWk
Graeffe's Method youtu.be/92oh5gYUP7Y
Generalized Newton's Method youtu.be/p0SBubUfwiI
Reference links:
"Applied Aerodynamics" by Bairstow books.google.com/books?id=GIUQAQAAMAAJ
"Elements of Numerical Analysis" by Henrici archive.org/details/elements-of-numerical-analysis-by-peter-henrici
"A Modified Bairstow Method for Multiple Zeros of a Polynomial" by F. M. Carrano doi.org/10.1090/S0025-5718-1973-0334492-5
Background music "Drifting at 432 Hz" by @UnicornHeads
#SoME2 #NumericalAnalysis #BairstowsMethod
Bairstow's 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 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 Bairstow's Original Problem
14:40 Oscar's Notes
15:24 Outro
Recommended Viewing:
Horner's Method youtu.be/zEvfkSuPqWk
Graeffe's Method youtu.be/92oh5gYUP7Y
Generalized Newton's Method youtu.be/p0SBubUfwiI
Reference links:
"Applied Aerodynamics" by Bairstow books.google.com/books?id=GIUQAQAAMAAJ
"Elements of Numerical Analysis" by Henrici archive.org/details/elements-of-numerical-analysis-by-peter-henrici
"A Modified Bairstow Method for Multiple Zeros of a Polynomial" by F. M. Carrano doi.org/10.1090/S0025-5718-1973-0334492-5
Background music "Drifting at 432 Hz" by @UnicornHeads
#SoME2 #NumericalAnalysis #BairstowsMethod
