Golden ratio | Optimization algorithms and methods | Search algorithms | Fibonacci numbers
The golden-section search is a technique for finding an extremum (minimum or maximum) of a function inside a specified interval. For a strictly unimodal function with an extremum inside the interval, it will find that extremum, while for an interval containing multiple extrema (possibly including the interval boundaries), it will converge to one of them. If the only extremum on the interval is on a boundary of the interval, it will converge to that boundary point. The method operates by successively narrowing the range of values on the specified interval, which makes it relatively slow, but very robust. The technique derives its name from the fact that the algorithm maintains the function values for four points whose three interval widths are in the ratio φ:1:φ where φ is the golden ratio. These ratios are maintained for each iteration and are maximally efficient. Excepting boundary points, when searching for a minimum, the central point is always less than or equal to the outer points, assuring that a minimum is contained between the outer points. The converse is true when searching for a maximum. The algorithm is the limit of (also described below) for many function evaluations. Fibonacci search and golden-section search were discovered by Kiefer (1953) (see also Avriel and Wilde (1966)). (Wikipedia).
Golden-section Search is a minimization algorithm that expands on the Fibonacci Search scheme described by J. Kiefer and S. M. Johnson. This interval-based numerical method improves on Ternary Search and Dichotomous Search be reusing interval points based on the golden ratio (phi). Code ca
From playlist Numerical Methods
Golden Ratio – Math that our eyes love!
TabletClass Math: https://tcmathacademy.com/ Math help with the golden ratio and golden rectangles. For more math help to include math lessons, practice problems and math tutorials check out my full math help program at https://tcmathacademy.com/ Math Notes: Pre-Algebra Notes:
From playlist GED Prep Videos
This video introduces the Golden ratio and provides several examples of where the Golden ratio appears. http:mathispower4u.com
From playlist Mathematics General Interest
Defining and Finding the Value of the Golden Ratio
This video focuses explores the great number Phi, also known as the Golden Ratio. The definition and exact value of the Golden Ratio is explained in this video. This Golden Ratio video series seeks to explore one of the most significant numbers in mathematics. This goal of this video se
From playlist Golden Ratio Series
Calculate Exact Value of Golden Ratio Raised to the 16th Power
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From playlist "Smarter In-A-Minute" Math on Shorts
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-veliz Chapters: 0:00 Intro 0:16 Scaffolding 0:3
From playlist Numerical Methods
Golden Ratio Visual Computation
This is a short, animated visual proof of showing how to compute the value of the golden ratio (which is the positive number satisfying x=1+1/x) without using the quadratic formula explicitly. Instead, we use a Tatami diagram and compute the areas of the included rectangles and squares to
From playlist Algebra
Lecture: Unconstrained Optimization (Derivative-Free Methods)
We introduce some of the basic techniques of optimization that do not require derivative information from the function being optimized, including golden section search and successive parabolic interpolation.
From playlist Beginning Scientific Computing
Fibonacci search scheme for finding the minimum of a function discovered by J. Kiefer and S. M. Johnson. This interval-based numerical method improves on Ternary Search and Dichotomous Search be reusing interval points based on ratios from the Fibonacci Sequence. Code can be found on GitHu
From playlist Numerical Methods
Dichotomous Search is an improved version of Ternary Search. This video describes the motivation and algorithm followed by a visualized example. Code can be found on GitHub https://www.github.com/osveliz/numerical-veliz *Correction* The numerical example used epsilon = 10^(-6) not 10^(-7)
From playlist Numerical Methods
Mathematical Games Hosted by Ed Pegg Jr. [Episode 3: Algebraic Number Magic]
Join Ed Pegg Jr. as he explores a variety of games and puzzles using Wolfram Language. In this episode, he features games and puzzles focusing on algebraic number magic. Follow us on our official social media channels. Twitter: https://twitter.com/WolframResearch/ Facebook: https://www.f
From playlist Mathematical Games Hosted by Ed Pegg Jr.
In this video, you’ll learn more about this particular topic. Visit https://edu.gcfglobal.org/en/jobsuccess/ for our text-based tutorial. We hope you enjoy!
From playlist Job Success
TryHackMe Ice - Walkthrough | Windows Privilege Escalation
In this video, I will be showing you how to pwn Ice on TryHackMe. We will cover the basics of Windows exploitation and post-exploitation. Our videos are also available on the decentralized platform LBRY: https://lbry.tv/$/invite/@HackerSploit:26 SUPPORT US: Patreon: https://www.patreon.c
From playlist Penetration Testing Bootcamp
Structs allow you to store more than one value inside of a single variable. They are similar to classes and objects in Java. In this session we'll learn how to declare structs and how to create them, access them, and put them into arrays.
From playlist C Programming, Fall 2022
How Is NASA Contacting Aliens? | Alien Life Documentary | Spark
Subscribe to Spark for more amazing science, tech and engineering videos - https://goo.gl/LIrlur With technology advancing faster than ever, and more and more discoveries being made every day, is the day we contact extraterrestrial life almost here? Follow us on Facebook: https://www.fa
From playlist All Things Aliens
Ternary Search is an interval-based divide-and-conquer algorithm for finding the minimum of a unimodal function. This video describes how to find a minimum when the derivative is know, defines unimodal, presents interval-based approaches for minimum finding, and visualizes the algorithm. E
From playlist Numerical Methods
Demystifying the Golden Ratio (Part 1)
Part 1 of series offering a mathematical explanation of why the Golden Ratio is commonly found in nature. In this video we discuss some basic aspects of the Golden Ratio, and its relationship with the Fibonocci numbers.
From playlist Demystifying the Golden Ratio