Lagrange Polynomials @OscarVeliz

Oscar Veliz | Lagrange Polynomials @OscarVeliz | Uploaded 13 years ago | Updated 9 minutes ago
Lagrange Polynomials for function approximation including simple examples.

Chapters
0:00 Intro
0:08 Lagrange Polynomials
0:51 Visualizing L2
1:00 Numeric Example
1:11 Example Visualized
1:27 Why Lagrange Works
1:47 Lagrange Accuracy
2:12 Error
2:59 Error Visualized
3:20 Error Bounds
4:08 Notes
4:25 Thanks For Watching

Further Viewing:
Inverse Quadratic Interpolation (part of Brent's Method) youtu.be/-bLSRiokgFk
Muller's Method youtu.be/XIIEjwtkONc
Cubic Spline youtu.be/f4iNbNRKZKU

#LagrangePolynomials #NumericalAnalysis

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