Brent's Minimization Method

Hybrid minimization algorithm combining Golden-section Search and Successive Parabolic Interpolation (Jarratt's Method) that is guaranteed to locate minima with superlinear convergence order. Example code https://github.com/osveliz/numerical-... Chapters: 0:00 Intro 0:16 Scaffolding 0:31 Motivation 1:17 Parabolic Interpolation Review 1:48 Renaming Variables 2:40 Brent's Method Algorithm 3:19 SPI Behaving? 4:08 Note on Updating 4:38 Brent's Method Visualization 6:02 Numerical Example 6:29 Note on Steps 6:43 MATLAB fminbnd 7:12 Minimum Strategy - Derivative 7:49 Note on Convergence Order 8:04 Oscar's Notes 8:39 Outro Suggested Viewing: Golden-section Search    • Golden-section Search   Successive Parabolic Interpolation - Jarratt's Method    • Successive Parabolic Interpolation - Jarra...   Minimization Playlist    • Minimization   Brent-Dekker Method    • Brent's Method   References: Brent's Book https://maths-people.anu.edu.au/~bren... MATLAB fminbnd documentation https://www.mathworks.com/help/matlab... SciPy documentation https://docs.scipy.org/doc/scipy/refe... GNU Octave fminbnd documentation https://octave.org/doc/v4.0.1/Minimiz... Background music "The Golden Present" by ‪@JesseGallagher‬ #GoldenSectionSearch #SuccessiveParabolicInterpolation #NumericalAnalysis