Uploaded May 2018 | Updated September 2026, 1 week ago

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How to find the Interval of Convergence for Newton-type methods such as Newton's Method, Secant Method, and Finite Difference Method including discussion on Damped Newton's Method and widening the convergence interval. Example code in R hosted on Github: github.com/osveliz/numerical-veliz

Chapters
0:00 Intro
0:08 Methods with Guaranteed Convergence
0:26 Newton-type Methods
0:42 Convergence vs Divergence Example
1:02 Example Visualized
1:31 Convergence Interval Visual
2:02 Finding Convergence Interval
2:20 Converge Interval Numerical Example
3:25 Widening the Interval
3:55 Widened Interval Visualized
4:31 Summary and Notes
5:14 Thank You

Further Viewing:
Newton's Method youtu.be/E24zUEKqgwQ
Newton Bisection Hybrid youtu.be/FD3BPTMGJds
Newton Fractal youtu.be/MWD2A0Vg2V0
Halley's Method youtu.be/3WiVGSy_084
Householder's Method youtu.be/F9DFewL0mho
Generalized Newton's Method youtu.be/p0SBubUfwiI

#NewtonsMethod #NumericalAnalysis