Uploaded April 2021 | Updated September 2026, 2 weeks ago

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Generalized Steffensen's Method for Simultaneous Nonlinear Systems originally credited to J. F. Traub. Video shows how to solve nonlinear systems by approximating the Jacobian. Example code on GitHub github.com/osveliz/numerical-veliz

Chapters
0:00 Prerequisites
0:20 Intro
0:40 Traub
1:24 Soleymani et al
1:58 Explaining Notation
2:32 1D Example
3:06 Two Methods - Same Method
3:20 System of Equations
3:27 Nonlinear System Example
4:42 Closer = Better ~J
5:03 Oscar's Notes
5:46 Thank You

Recommended Viewing
Steffensen's Method with Aitken's Δ² youtu.be/BTYTj0r5PZE
Generalized Aitken-Steffensen youtu.be/-x9_fSNrX3w
Newton's Method for Systems of Nonlinear Equations youtu.be/m_nfoUz-PNY
Generalized Finite Difference Method youtu.be/G25sGOWkOuQ
Broyden's Method youtu.be/UlLGzW-KjHs

References
"Iterative Methods for the Solution of Equations" by J. F. Traub archive.org/details/iterativemethods0000trau
"A Class of Steffensen-Type Iterative Methods for Nonlinear Systems" by Soleymani et. al. doi.org/10.1155/2014/705375

Background music "The Golden Present" by @JesseGallagher

#Steffensen'sMethod #NumericalAnalysis #NonlinearSystem