Uploaded March 2011 | Updated September 2026, 2 weeks ago

Bisection Method for finding roots of functions including simple examples and an explanation of the order.

Chapters
0:00 Intro
0:14 Bisection Method
1:06 Visual Example
1:49 Difficult Functions
2:14 Order
3:16 Finding Order Example
3:38 Maximum Number of Iterations
4:28 Thanks For Watching

Further Viewing:
False Position Method: youtu.be/pg1I8AG59Ik
Brent-Dekker Method: youtu.be/-bLSRiokgFk
Newton-Bisection Hybrid: youtu.be/FD3BPTMGJds

#BisectionMethod #NumericalAnalysis

$Wilfs Method - Global Bisection #SoME5 Wilfs Method Global Bisection for finding roots of polynomials in the complex plane. Example code hosted on GitHub https://github.com/osveliz/numerical-veliz Clarification and Correction: The V(x) test example on x^2-x-1 is used on the Sturm Sequence of the given polynomial f_n = {x^2-x-1, 2x-1, 5/4}. Therefore, the four test points result in the series: f_n(-1) = {1, -3, 5/4}, f_n(0) = {-1, -1, 5/4}, f_n(1) = {-1, 1, 5/4}, & f_n(2) = {1, 3, 5/4} Applying the V(x) function looks at the sign changes in the sequence so - → + counts as does + → - but not - → - nor + → +. Going from non-zero to zero and vice versa also counts. Giving these results: V(-1) = {+,-,+} = 2, V(0) = {-, -, +} = 1, V(1) = {-, +, +} = 1, & V(2) = {+, +, +} = 0 Some of these values did not appear in the final rendering of the video. Chapters: 0:00-0:36 Intro 0:37-0:58 Lehmer-Schur video 0:59-2:37 Wilf Search 2:38-4:49 Sturm Sequence 4:50-5:50 Fouriers Approach 5:51-6:44 Historical Context 6:45-9:01 Adapting for Complex Plane 9:02-10:02 Oscars Thoughts 10:03-10:18 Outro Recommended Viewing: Lehmer-Schur https://youtu.be/hT0EY2rxLlQ Bernoullis Method https://youtu.be/zB_pQJWnhTc Jenkins-Traub https://youtu.be/3_yxAnhLiAk Bairstows Method https://youtu.be/iUGEk6kngFw Graeffes Method https://youtu.be/92oh5gYUP7Y Aberth-Ehrlich https://youtu.be/XIzCzfMDSzk Durand-Kerner https://youtu.be/5JcpOj2KtWc Horners Method https://youtu.be/zEvfkSuPqWk Generalized Bisection for Systems of Nonlinear Equations https://youtu.be/rMg61nfkZ3M Bisection Method https://youtu.be/MlP_W-obuNg References: Wilf, Herbert S. A global bisection algorithm for computing the zeros of polynomials in the complex plane. Journal of the ACM (JACM) 25.3 (1978): 415-420. Sturm Biography https://mathshistory.st-andrews.ac.uk/Biographies/Sturm/ Heindel, Lee E. Integer arithmetic algorithms for polynomial real zero determination. Proceedings of the second ACM symposium on Symbolic and algebraic manipulation. 1971. Pinkert, James R. An exact method for finding the roots of a complex polynomial. ACM Transactions on Mathematical Software (TOMS) 2.4 (1976): 351-363. Background music Drifting at 432 Hz by @UnicornHeads #numericalanalysis #rootfinding #bisectionmethod$

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