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-v...

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    • Video Mistakes II: The Sequel   for a small correction.

Recommended Viewing:
Fixed Point Iteration    • Fixed Point Iteration  
Fixed Point Iteration Q&A    • Fixed Point Iteration Q&A  
Generalized Aitken-Steffensen    • Generalized Aitken-Steffensen Method  
Generalized Newton's Method    • Newton's Method for Systems of Nonlin...  

Reference Link:
"Elements of Numerical Analysis" by Peter Henrici https://archive.org/details/ElementsO...
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