Oscar Veliz | What is Order of Convergence? @OscarVeliz | Uploaded 4 years ago | Updated 2 minutes ago
Converge order and error reduction can be confusing but this video breaks it down and provides examples showing how order relates to speed and runtime. It also explains how order of convergence relates to Big O. Watching the other videos on this channel can be helpful but is not necessary. Example root finding method code for all of the above methods can be found on github github.com/osveliz/numerical-veliz
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Chapters
00:00 - Intro
00:19 - Order Montage
00:54 - Error Definition
01:11 - Introduction of α
01:35 - α equation
01:41 - α example 1 Bisection
02:09 - Solving for M
02:36 - α example 2 False Position
03:13 - α example 3 Newton
03:41 - On Function Calls
04:19 - α with iterations and runtime
05:02 - Note on previous example
05:23 - Generalized operation count
06:28 - How fast is linear?
07:29 - How fast is quadratic?
09:33 - Digits of accuracy
10:15 - Distance impacts α
10:52 - Big O brief intro
11:37 - Big O of Bisection
12:09 - Big O of Newton and Halley
13:02 - Oscar's Notes
13:47 - Thank You
The other methods referenced in this video include: Fixed Point Iteration Method, Bisection Method, False Position Method - Regula Falsi, Newton's Method, Steffensen's Method, Wegstein's Method, Muller's Method, Durand-Kerner Method, Secant Method, Householder's Method, and Halley's Method. All of these method can be found in this root finding playlist youtube.com/playlist?list=PLb0Tx2oJWuYIpNE23qYHGQD42TIR3ThNz
#ConvergenceOrder #NumericalAnalysis
Converge order and error reduction can be confusing but this video breaks it down and provides examples showing how order relates to speed and runtime. It also explains how order of convergence relates to Big O. Watching the other videos on this channel can be helpful but is not necessary. Example root finding method code for all of the above methods can be found on github github.com/osveliz/numerical-veliz
Become a GitHub Sponsor github.com/sponsors/osveliz
Chapters
00:00 - Intro
00:19 - Order Montage
00:54 - Error Definition
01:11 - Introduction of α
01:35 - α equation
01:41 - α example 1 Bisection
02:09 - Solving for M
02:36 - α example 2 False Position
03:13 - α example 3 Newton
03:41 - On Function Calls
04:19 - α with iterations and runtime
05:02 - Note on previous example
05:23 - Generalized operation count
06:28 - How fast is linear?
07:29 - How fast is quadratic?
09:33 - Digits of accuracy
10:15 - Distance impacts α
10:52 - Big O brief intro
11:37 - Big O of Bisection
12:09 - Big O of Newton and Halley
13:02 - Oscar's Notes
13:47 - Thank You
The other methods referenced in this video include: Fixed Point Iteration Method, Bisection Method, False Position Method - Regula Falsi, Newton's Method, Steffensen's Method, Wegstein's Method, Muller's Method, Durand-Kerner Method, Secant Method, Householder's Method, and Halley's Method. All of these method can be found in this root finding playlist youtube.com/playlist?list=PLb0Tx2oJWuYIpNE23qYHGQD42TIR3ThNz
#ConvergenceOrder #NumericalAnalysis
