Uploaded January 2022 | Updated September 2026, 2 weeks ago

---

False Position Method for Nonlinear Systems (aka Generalized Regula Falsi) along with two Alternative Secant Methods. Includes discussion of history and primary sources along with numeric examples and visualizations. Example code hosted on GitHub github.com/osveliz/numerical-veliz

Chapters:
0:00 Scaffolding
0:25 Korganoff
1:02 Robinson
1:32 Some History
1:50 Robinson Continued
2:51 Robinson versus Secant
3:27 Nonlinear System Example
4:16 On Notation
4:37 Efficient Orthogonal Matrix
4:53 Generalized False Position Method
5:18 Oscar's Notes
8:38 Outro

Recommended Viewing:
Secant Method youtu.be/_MfjXOLUnyw
Generalized Secant Method youtu.be/p2OPlnHJPNI
Broyden's Method youtu.be/UlLGzW-KjHs
Generalized Steffensen's Method youtu.be/ndf2vjXjXzQ
Generalized Finite Difference Method youtu.be/G25sGOWkOuQ
False Position Method youtu.be/pg1I8AG59Ik

Reference links:
"Some Efficient Algorithms for Solving Systems of Nonlinear Equations" by Richard P. Brent doi.org/10.1137/0710031
"Iterative Solution of Nonlinear Equations in Several Variables" by Ortega and Rheinboldt books.google.com/books/about/Iterative_Solution_of_Nonlinear_Equation.html?id=UEFRfUZBpUEC
"Méthodes de calcul numérique: Algèbre non linéaire, Vol 1" by André Korganoff, worldcat.org/title/methodes-de-calcul-numerique/oclc/848108709
"Interpolative Solution of Systems of Nonlinear Equations" by Stephen M. Robinson epubs.siam.org/doi/abs/10.1137/0703057

Background music "Drifting at 432 Hz" by @UnicornHeads
#NumericalAnalysis #FalsePosition #SecantMethod