Generalized Aitken-Steffensen Method

Generalized Aitken's delta-squared method and Generalized Steffensen's Method applying Fixed Point Iteration to Systems of Nonlinear Equations. Video goes step-by-step to derive Generalized Aitken-Steffensen and discusses induced and accelerated convergence behavior as well as quadratic order. Example code github: http://github.com/osveliz/numerical-v...

Chapters
0:00 Intro
0:40 Motivation
2:32 Solve for X*
3:10 Generalized Aitken
3:44 Generalized Aitken Example
4:10 Generalized Aitken-Steffensen Method
4:40 Generalized Aitken-Steffensen Method Example 1
5:02 Generalized Aitken-Steffensen Method Example 2
5:26 Henrici
5:59 On Order & Proving Convergence
6:31 Proof Intuition
6:55 Notes
7:40 Thank You

Recommended Viewing:
Fixed Point Iteration    • Fixed Point Iteration  
Fixed Point Iteration Q&A    • Fixed Point Iteration Q&A  
Steffensen's Method with Aitken's Δ²    • Steffensen's Method with Aitken's Δ²  
Fixed Point Iteration Systems of Equations    • Fixed Point Iteration System of Equat...  
Generalized Newton's Method    • Newton's Method for Systems of Nonlin...  
Generalized Steffensen's Method    • Steffensen's Method for Systems of No...  

References:
Elements of Numerical Analysis by Peter Henrici https://archive.org/details/ElementsO...
Tatsuo Noda "The Steffensen Iteration Method for Systems of Nonlinear Equations" https://projecteuclid.org/euclid.pja/... https://projecteuclid.org/euclid.pja/... and https://projecteuclid.org/euclid.pja/...
Yves Nievergelt "Aitken's and Steffensen's Accelerations in Several Variables" https://link.springer.com/article/10....

#AitkensDeltaSquaredMethod #SteffensensMethod #NumericalAnalysis