Fixed Point Iteration System of Equations with Banach

Fixed Point Iteration Method to solve Systems of Nonlinear Equations with discussion of Banach Fixed Point Theorem, finding the Jacobian, convergence, and order. Example code on GitHub: http://github.com/osveliz/numerical-veliz

Chapters:
00:00 Intro
00:25 Systems of Equations
00:33 Solving Nonlinear Systems
01:03 Fixed Point Iteration
01:26 Rewriting Equations
02:03 Example 1
02:23 Visualized Example
03:12 Measuring Distance and Norm
03:45 End Conditions
04:09 Different Combinations of Rewrites
04:45 When Does it Converge?
05:10 Banach Fixed Point Theorem
05:56 The Jacobian
06:48 Contraction Mapping Test
07:24 Contraction Mapping Test Examples
08:20 Notes on the Contraction Mapping Test
09:06 Order of Convergence
09:41 Exact Order
10:31 Summary
10:49 Thank You

See Video Mistakes II: The Sequel https://youtu.be/YEUbzqkJBf0 for a small correction.

Recommended Viewing:
Fixed Point Iteration https://youtu.be/OLqdJMjzib8
Fixed Point Iteration Q&A https://youtu.be/FyCviw2ZA2o
Generalized Aitken-Steffensen https://youtu.be/-x9_fSNrX3w
Generalized Newton's Method https://youtu.be/p0SBubUfwiI

Reference Link:
"Elements of Numerical Analysis" by Peter Henrici https://archive.org/details/ElementsOfNumericalAnalysis/page/n57
#FixedPointIteration #NumericalAnalysis

Видео Fixed Point Iteration System of Equations with Banach канала Oscar Veliz