Uploaded March 2021 | Updated September 2026, 2 weeks ago
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 github.com/osveliz/numerical-veliz
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 youtu.be/_MfjXOLUnyw
Newton's Method for Systems of Nonlinear Equations youtu.be/m_nfoUz-PNY
Broyden's Method youtu.be/UlLGzW-KjHs
Generalized False Position & Alternative Secant Methods youtu.be/c2kSfJ8of7E
References
"The Secant method for simultaneous nonlinear equations" by Phillip Wolfe 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 doi.org/10.1145/321217.321224
"An Algorithm for Solving Non-Linear Equations Based on the Secant Method" by J. G. P. Barnes doi.org/10.1093/comjnl/8.1.66
"Some Efficient Algorithms for Solving Systems of Nonlinear Equations" by Richard P. Brent doi.org/10.1137/0710031
"The Computational Complexity of Iterative Methods for Systems of Nonlinear Equations" by Richard Brent doi.org/10.1007/978-1-4684-2001-2_7
Background music "The Golden Present" by @JesseGallagher
#SecantMethod #NumericalAnalysis #NonlinearSystem
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 github.com/osveliz/numerical-veliz
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 youtu.be/_MfjXOLUnyw
Newton's Method for Systems of Nonlinear Equations youtu.be/m_nfoUz-PNY
Broyden's Method youtu.be/UlLGzW-KjHs
Generalized False Position & Alternative Secant Methods youtu.be/c2kSfJ8of7E
References
"The Secant method for simultaneous nonlinear equations" by Phillip Wolfe 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 doi.org/10.1145/321217.321224
"An Algorithm for Solving Non-Linear Equations Based on the Secant Method" by J. G. P. Barnes doi.org/10.1093/comjnl/8.1.66
"Some Efficient Algorithms for Solving Systems of Nonlinear Equations" by Richard P. Brent doi.org/10.1137/0710031
"The Computational Complexity of Iterative Methods for Systems of Nonlinear Equations" by Richard Brent doi.org/10.1007/978-1-4684-2001-2_7
Background music "The Golden Present" by @JesseGallagher
#SecantMethod #NumericalAnalysis #NonlinearSystem
