Secant Method for Systems of Nonlinear Equations

Generalized Secant Method for Simultaneous Nonlinear Systems originally credited to Wolfe and Bittner. Lesson shows how to solve nonlinear systems without the Jacobian, nor the need to approximate it, in a straightforward and visual manner. Example code on GitHub https://www.github.com/osveliz/numeri...

Chapters
0:00 Intro
0:15 Prerequisites
0:25 Secant Method Recap
0:45 Literature
1:00 Secant Method Alternative
2:12 Two Methods - Same Method
2:27 Nonlinear System + Example
2:49 Generalized Secant Method Visualized
4:12 Numeric Example
4:28 Order!
4:50 "A Class of Secant Methods"
5:31 Oscar's Notes
6:05 Thank You

Recommended Viewing
Secant Method    • Secant Method  
Newton's Method for Systems of Nonlinear Equations    • Видео  
Broyden's Method    • Broyden's Method  
Generalized False Position & Alternative Secant Methods    • Generalized False Position & Alternat...  

References
"The Secant method for simultaneous nonlinear equations" by Phillip Wolfe https://doi.org/10.1145/368518.368542
"Eine Verallgemeinerung des Sekantenverfahrens (regula falsi) zur naherungsweisen Berechnung der Nullstellen eines nichtlinearen Gleichungssystems" by Von Leonhard Bittner borrowed from Technische Universität Dresden
"Convergence of Multipoint Iterative Methods" by Leonard Tornheim https://doi.org/10.1145/321217.321224
"An Algorithm for Solving Non-Linear Equations Based on the Secant Method" by J. G. P. Barnes https://doi.org/10.1093/comjnl/8.1.66
"Some Efficient Algorithms for Solving Systems of Nonlinear Equations" by Richard P. Brent https://doi.org/10.1137/0710031
"The Computational Complexity of Iterative Methods for Systems of Nonlinear Equations" by Richard Brent https://doi.org/10.1007/978-1-4684-20...

Background music "The Golden Present" by ‪@JesseGallagher‬

#SecantMethod #NumericalAnalysis #NonlinearSystem