In mathematics, the bisection method is a root-finding method that applies to any continuous function for which one knows two values with opposite signs. The method consists of repeatedly bisecting the interval defined by these values and then selecting the subinterval in which the function changes sign, and therefore must contain a root. It is a very simple and robust method, but it is also relatively slow. Because of this, it is often used to obtain a rough approximation to a solution which is then used as a starting point for more rapidly converging methods. The method is also called the interval halving method, the binary search method, or the dichotomy method. For polynomials, more elaborate methods exist for testing the existence of a root in an interval (Descartes' rule of signs, Sturm's theorem, Budan's theorem). They allow extending the bisection method into efficient algorithms for finding all real roots of a polynomial; see Real-root isolation. (Wikipedia).
Bisection Method for finding roots of functions including simple examples and an explanation of the order. Chapters 0:00 Intro 0:14 Bisection Method 1:06 Visual Example 1:49 Difficult Functions 2:14 Order 3:16 Finding Order Example 3:38 Maximum Number of Iterations 4:28 Thanks For Watchin
From playlist Root Finding
Bisection Method | Lecture 13 | Numerical Methods for Engineers
Explanation of the bisection method for finding the roots of a function. Join me on Coursera: https://www.coursera.org/learn/numerical-methods-engineers Lecture notes at http://www.math.ust.hk/~machas/numerical-methods-for-engineers.pdf Subscribe to my channel: http://www.youtube.com/us
From playlist Numerical Methods for Engineers
Generalized Bisection Method for Systems of Nonlinear Equations
Generalization of the Bisection Method for solving systems of equations. This lesson explains the algorithm for a 2 dimension example based on Harvey-Stenger's approach using bisecting triangles. It includes a visualization of the method in action on an example nonlinear system. Other meth
From playlist Solving Systems of Nonlinear Equations
Calculus: Bisection, Secant, and Newton
This video provides a unique view into what Calculus is, what it can be used for, and how it can be used in the real world. To illustrate how these three concepts are all connected, I consider the two very important examples of finding the solution of a complicated equation and finding the
From playlist Calculus
Bisection Method (2 of 2: How to Halve the Interval)
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From playlist Further Work with Functions (related content)
Mathematica Tutorial 23 - The bisection method for solving an equation
In this Mathematica tutorial you will learn about the bisection method for solving an equation and how to use it. The bisection method is a slow but robust method for solving an equation numerically. *** SUBSCRIBE FOR MORE VIDEOS *** Never miss a daily video about Mathematics and Mathem
From playlist Mathematica Tutorials
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
Solving a trig function with sine and cosine
👉 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 of the solutions to an equation as well as within the unit circle
👉 Learn how to solve trigonometric equations. There are various methods that can be used to evaluate trigonometric identities, they include by factoring out the GCF and simplifying the factored equation. Another method is to use a trigonometric identity to reduce and then simplify the give
From playlist Solve Trigonometric Equations
Newton Bisection Hybrid (Newt-Safe)
Newton Bisection Hybrid Method for root finding. Example code available at https://www.github.com/osveliz/numerical-veliz Chapters 0:00 Intro 0:26 Viewer Request 0:49 Numerical Recipes 1:12 Numerical Methods That Work 1:54 Motivation Examples 3:04 Problems with Newton Recap 3:17 Newt-Safe
From playlist Root Finding
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
False Position Method - Regula Falsi
False Position Method (Regula Falsi) for finding roots of functions. Includes comparison against Bisection and discussion of order. Sample code in C available on GitHub https://github.com/osveliz/numerical-veliz Chapters 0:00 Intro 0:21 Regula Falsi Family Tree 0:33 False Position Method
From playlist Root Finding
Converge order and error reduction can be confusing but this video breaks it down and provides examples showing how order relates to speed and runtime. It also explains how order of convergence relates to Big O. Watching the other videos on this channel can be helpful but is not necessary.
From playlist Root Finding
RubyConf 2017: "RSpec no longer works with ActiveRecord" by Sam Phippen
RubyConf 2017: "RSpec no longer works with ActiveRecord" by Sam Phippen Sometimes an email appears in front of you in your inbox that immediately grabs your attention. For me, this was the case with a particularly scarily titled RSpec Mocks bug. In this talk, you'll hear a story of inves
From playlist RubyConf 2017
Marina Iliopoulou: Three polynomial methods for point counting, Lecture II
During these lectures, we will describe (a) the polynomial method that Dvir developed to solve the Kakeya problem in finite fields, (b) polynomial partitioning, developed by Guth and Katz to solve the Erdös distinct distances problem in the plane, and (c) the slice rank method, developed b
From playlist Harmonic Analysis and Analytic Number Theory
Order of Convergence |Lecture 16 | Numerical Methods for Engineers
Definition of the order of convergence of a root-finding method. Join me on Coursera: https://www.coursera.org/learn/numerical-methods-engineers Lecture notes at http://www.math.ust.hk/~machas/numerical-methods-for-engineers.pdf Subscribe to my channel: http://www.youtube.com/user/jchas
From playlist Numerical Methods for Engineers
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