Householder's Method @OscarVeliz

Uploaded October 2019 | Updated September 2026, 2 weeks ago

Householder's Method for finding roots of equations including history, derivation, examples, and fractals. Example code is available on GitHub github.com/osveliz/numerical-veliz

Chapters
0:00 Intro
0:25 Derivation
1:58 History
2:34 Householder's Method
4:07 Householder's Method Example
4:41 Higher Order Householder's Method Examples
5:30 Principles of Numerical Analysis
6:03 Householder Fractals
8:10 Summary
8:41 Thank You

Suggested Videos:
Newton's Method youtu.be/E24zUEKqgwQ
Newton's Method Convergence Interval youtu.be/zyXRo8Qjj0A
Newton Fractals youtu.be/MWD2A0Vg2V0
Halley's Method youtu.be/3WiVGSy_084
Newton-Bisection Hybrid youtu.be/FD3BPTMGJds

Reference:
Householder's book archive.org/details/principlesofnume030218mbp/page/n143
Petković's paper sciencedirect.com/science/article/pii/S0377042709006347

#HouseholdersMethod #NumericalAnalysis

$Householders Method Householders Method for finding roots of equations including history, derivation, examples, and fractals. Example code is available on GitHub https://github.com/osveliz/numerical-veliz Chapters 0:00 Intro 0:25 Derivation 1:58 History 2:34 Householders Method 4:07 Householders Method Example 4:41 Higher Order Householders Method Examples 5:30 Principles of Numerical Analysis 6:03 Householder Fractals 8:10 Summary 8:41 Thank You Suggested Videos: Newtons Method https://youtu.be/E24zUEKqgwQ Newtons Method Convergence Interval https://youtu.be/zyXRo8Qjj0A Newton Fractals https://youtu.be/MWD2A0Vg2V0 Halleys Method https://youtu.be/3WiVGSy_084 Newton-Bisection Hybrid https://youtu.be/FD3BPTMGJds Reference: Householders book https://archive.org/details/principlesofnume030218mbp/page/n143 Petkovićs paper https://www.sciencedirect.com/science/article/pii/S0377042709006347 #HouseholdersMethod #NumericalAnalysis$

Approximating the Jacobian: Finite Difference Method for Systems of Nonlinear Equations

$Newton Fractals Using Newtons Method to create Fractals by plotting convergence behavior on the complex plane. Functions used in this video include arctan(z), z^3-1, sin(z), z^8-15z^4+16. Example code and images available at https://github.com/osveliz/numerical-veliz Correction: The derivative of arctan(x) should be 1/(1+x^2). This error is only impacts the slides, not the numerical examples nor fractals which used the correct derivative. A video covering this mistake can be found here https://youtu.be/4jw0cjddmB8 Chapters 0:00 Intro 0:16 Convergence Interval Recap 0:42 Imaginary Numbers 1:05 Newtons Method in Complex Plane 1:29 Basin of Convergence 1:38 Arctangent Fractal 1:50 Newton Fractal 2:10 Why Fractals Emerge 2:54 Example z^3-1 4:07 Example sin(z) 4:33 Example z^8+15z^4-16 4:50 Generalized Newton Fractal 5:05 Generalized Newton Fractal Examples 6:16 Summary 6:42 Thank You Further Viewing: Newtons Method https://youtu.be/E24zUEKqgwQ Newtons Method Interval of Convergence https://youtu.be/zyXRo8Qjj0A Newton Bisection Hybrid (Newt-Safe) https://youtu.be/FD3BPTMGJds Laguerres Method and Fractal https://youtu.be/blOARV4lnIM Halleys Method and Fractal https://youtu.be/3WiVGSy_084 Generalized Newtons Method https://youtu.be/p0SBubUfwiI Further Reading: Numerical Recipes http://numerical.recipes/ Wikipedia https://en.wikipedia.org/wiki/Newton_fractal #Fractal #NewtonsMethod #NumericalAnalysis$