In numerical analysis, Brent's method is a hybrid root-finding algorithm combining the bisection method, the secant method and inverse quadratic interpolation. It has the reliability of bisection but it can be as quick as some of the less-reliable methods. The algorithm tries to use the potentially fast-converging secant method or inverse quadratic interpolation if possible, but it falls back to the more robust bisection method if necessary. Brent's method is due to Richard Brent and builds on an earlier algorithm by Theodorus Dekker. Consequently, the method is also known as the Brent–Dekker method. Modern improvements on Brent's method include Chandrupatla's method, which is simpler and faster for functions that are flat around their roots; Ridders' method, which performs exponential interpolations instead of quadratic providing a simpler closed formula for the iterations; and the ITP method which is a hybrid between regula-falsi and bisection that achieves optimal worst-case and asymptotic guarantees. (Wikipedia).
Dekker's Method, Inverse Quadratic Interpolation, and Brent's Method including example, code, and discussion of order. GitHub https://github.com/osveliz/numerical-veliz Chapters 00:00 Intro 00:12 Secant Method Recap 00:37 Bisection Method Recap 00:54 Dekker's Method History 01:35 Dekker's
From playlist Root Finding
More videos like this online at http://www.theurbanpenguin.com We now look at how we can use and define methods in ruby to help keep the code tidy and concise. This also helps with readability of the code and later maintenance. In the example we use we take the decimal to ip address conver
From playlist RUBY
Newton's Method for Systems of Nonlinear Equations
Generalized Newton's method for systems of nonlinear equations. Lesson goes over numerically solving multivariable nonlinear equations step-by-step with visual examples and explanation of the Jacobian, the backslash operator, and the inverse Jacobian. Example code in MATLAB / GNU Octave on
From playlist Newton's 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-veliz Chapters: 0:00 Intro 0:16 Scaffolding 0:3
From playlist Numerical Methods
Euler’s method - How to use it?
► My Differential Equations course: https://www.kristakingmath.com/differential-equations-course Euler’s method is a numerical method that you can use to approximate the solution to an initial value problem with a differential equation that can’t be solved using a more traditional method,
From playlist Differential Equations
Solving a trigonometric equation with applying pythagorean identity
👉 Learn how to solve trigonometric equations. There are various methods that can be used to evaluate trigonometric equations, they include factoring out the GCF and simplifying the factored equation. Another method is to use a trigonometric identity to reduce and then simplify the given eq
From playlist Solve Trigonometric Equations by Factoring
How to find all the solutions to a trigonometric equation
👉 Learn how to solve trigonometric equations. There are various methods that can be used to evaluate trigonometric equations, they include factoring out the GCF and simplifying the factored equation. Another method is to use a trigonometric identity to reduce and then simplify the given eq
From playlist Solve Trigonometric Equations by Taking the Square Root
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
From playlist Numerical Methods
How Newton's method solves multiple equations at once
This video explains how Newton's method (also called the Newton-Raphson method) can solve more than one equation simultaneously. MDO Lab: https://mdolab.engin.umich.edu/ Engineering Design Optimization: https://mdobook.github.io/ Animations done using Manim: https://docs.manim.community/e
From playlist Summer of Math Exposition 2 videos
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
Secant Method for Systems of Nonlinear Equations
Generalized Secant Method for Simultaneous Nonlinear Systems originally credited to Wolfe and Bittner. Lesson shows how to solve nonlinear systems without the Jacobian, nor the need to approximate it, in a straightforward and visual manner. Example code on GitHub https://www.github.com/osv
From playlist Solving Systems of Nonlinear Equations
This video explains Newton's Method and provides an example. It also shows how to use the table feature of the graphing calculator to perform the calculations needed for Newton's Method. http://mathispower4u.wordpress.com/
From playlist Newton’s Method and L’Hopital’s Rule
Lone Star Restoration: Meet Brent Hull | History
Meet Brent Hull, a unique historical architectural restorer who stays true to centuries-old tools and methods, in this web exclusive. #LoneStarRestoration Subscribe for more from Lone Star Restoration and other great HISTORY shows: http://histv.co/SubscribeHistoryYT Find out more about t
From playlist Lone Star Restoration | Official Series Playlist | History
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
Labeling a System by Solving Using Elimination Method
👉Learn how to solve a system (of equations) by elimination. A system of equations is a set of equations which are collectively satisfied by one solution of the variables. The elimination method of solving a system of equations involves making the coefficient of one of the variables to be e
From playlist Solve a System of Equations Using Elimination | Medium
Can we create the "perfect" farm? - Brent Loken
Explore the innovative ways countries are revolutionizing farming to ensure we can feed humanity in a way that works with the environment. -- About 10,000 years ago, humans began to farm. This agricultural revolution was a turning point in our history and enabled the existence of civiliz
From playlist New TED-Ed Originals
Lone Star Restoration: An Insider's Look at Brent Hull | History
Brent Hull admittedly "geeks out" when it comes to historical architecture - his employees and even his wife poke fun at his appreciation for every detail in this web exclusive. #LoneStarRestoration Subscribe for more from Lone Star Restoration and other great HISTORY shows: http://histv.
From playlist Lone Star Restoration | Official Series Playlist | History
Lone Star Restoration: Brent's Favorite Tools | History
Brent Hull describes why historic hand tools, materials, and methods have been around for so long and why he and his team of craftsmen at Hull Historical still use them in this web exclusive. #LoneStarRestoration Subscribe for more from Lone Star Restoration and other great HISTORY shows:
From playlist Lone Star Restoration | Official Series Playlist | History
Newton's method for finding zeroes | Real numbers and limits Math Foundations 83 | N J Wildberger
Newton, the towering scientific figure of the 17th century, discovered a lovely method for finding approximate solutions to equations, involving iterated constructions of tangent lines and their intersections. We describe this method in general and then apply it to the simplest and most fa
From playlist Math Foundations