Successive Parabolic Interpolation - Jarratt's Method скачать в хорошем качестве

Successive Parabolic Interpolation - Jarratt's Method

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 #SuccessiveParabolicInterpolation #NumericalAnalysis