Successive Parabolic Interpolation - Jarratt's Method

Описание: Optimization method for finding extrema of functions using three points to create a parabola that is then used to find the next approximation to the solution. This lesson visualizes the behavior of the method with numeric examples as well as its convergence through fractals. Based off the paper "An iterative method for locating turning points" by P. Jarratt. Example code https://github.com/osveliz/numerical-...

Chapters:
0:00 Intro
0:21 Scaffolding
0:42 Richard P. Brent
1:01 An Iterative Method for Locating Turning Points
1:33 Graphing
1:46 Create a Quadratic
1:58 Finding the Next Point
2:35 The Next Iteration
2:22 Derivative is Zero
2:56 Avoid Calculating L_2
3:32 Jarratt's Method
3:47 Example
4:10 Fractal Scaffolding
4:20 Complex Plane Discussion
5:47 Jarratt Fractal z^4/4 - z
6:33 Jarratt Fractal -cos(z)
6:55 Jarratt Fractal z^9/9 + 3z^5 - 16z
7:52 Jarratt's Notes
8:32 Oscar's Notes
9:00 Thank You

Suggested Viewing:
Ternary Search    • Ternary Search  
Lagrange Polynomials    • Lagrange Polynomials  
Muller's Method    • Muller's Method  
Inverse Quadratic Interpolation    • Brent's Method  
Brent's Minimization Method    • Brent's Minimization Method  

References:
Jarratt's paper https://doi.org/10.1093/comjnl/10.1.82
Brent's Book https://maths-people.anu.edu.au/~bren...

Background music "The Golden Present" by ‪@JesseGallagher‬

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