# Bisection method Definition and 29 Threads

In mathematics, the bisection method is a root-finding method that applies to any continuous functions 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 elaborated 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 bisection method into efficient algorithms for finding all real roots of a polynomial; see Real-root isolation.

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1. ### I Why is (a+b)/2 not recommended in the Bisection method?

The image attached above from a textbook, explains that we should refrain from using (a+b)/2 while applying Bisection method but I am unable to get the reason why it is asking to do so? While the image above is from another textbook. This book uses (a+b)/2. I am really confused by two different...

12. ### MATLAB Script for Bisection Method

Homework Statement Not really for homework, but it is a script I am working on. It involves utilizing the Bisection Method for solving equations in one variable. However, I cannot seem to get it to work properly. It seems to enter the while loop and become stuck their. When I execute it by...
13. ### Bisection method and multiple roots

Hello, I have a polynomial of order n and I want to find all it's roots with bisection method. Is it possible? I already wrote an algorithm to find a root and it's works nice for finding one of it's roots, but what about others? Nikola
14. ### Fortran What's causing my Fortran bisection method to give incorrect results?

I'm rusty with fortran and programming in general. I can't see my "error" in a code that I wrote from scratch. Basically I wanted to get some fun and solve for a temperature in thermodynamics where I must get "T_f" which appear in a transcendental equation: ##A\ln \left ( \frac{T_f^2}{T_1T_2}...
15. ### Write a program using Bisection method and method of false position.

Hello everyone. I'm new here and I'm not not a computer science student. But, I have to take programming to complete my degree. So, now I'm in a great depression about this assignment. My lecturer ask me to write a program to find root of an equation f(x)=0 for specific f. Both methods are...
16. ### Fortran What's Wrong with My Fortran 90 Bisection Method Code?

Bisection method for the equation x3−2x−2 = 0 which has a single root between x=−4 and x = 2. here's the code I have program bisection2 implicit none real :: fxa, xnew, xu, xl, fxb, fnew xu=4 xl=2 1 xnew=(xu+xl)/2 fxa=(xnew**3-(2*xnew)-2) fxb=(xl**3-(2*xl)-2)...
17. ### MATLAB Implementing Bisection Method in Matlab: Troubleshooting Error Message

Here is the code I have, but I keep getting the error message: Undefined function 'f' for input arguments of type 'double'. I don't know what I have that is causing this. Does anybody see what's wrong with my code? MaxIt = 1000; epsilon = 10^-5; a=1; b=2; c = (b+a)/2; NumIt = 0...
18. ### Comp Sci Bisection Method for Finding Roots of x^3+4x^2-x-1 in C++

Homework Statement find the roots ( interval halving ) , I want to know how to make a condition statement that when fun3 be less than 0.001 and then loop will stop and i get the root .(here in my code i don't know why the loop doesn't work as it should .. Homework Equations the...
19. ### Bisection Method in C to Find Root of x^4+x^3-12x^2-2x+10

Hi guys, I'm doing an assignment for working out a certain root of a given function, x^4+x^3-12x^2-2x+10, to a precision of 10-6. We are asked to give two limits of where we want to find a root between but I'm getting stuck. I was just wondering if any of you could look at my code and maybe...
20. ### Comp Sci FORTRAN Help: Bisection Method & Roots of Functions

Homework Statement The purpose of this program is to calculate the approximate roots of the Sine function on given intervals. The intervals are input by the user, and then the do loop continues until the condition (m becomes very close to 0 or equals 0) is met. The Attempt at a Solution...
21. ### Convergence of Bisection Method

Homework Statement Show that the Bisection Method converges linearly with K = 1/2 Homework Equations Note that x(sub n) converges to the exact root r with an order of convergence p if: lim(n->oo) (|r - x(n + 1)|) / (|r - x(n)|^p) = lim(n->oo) (|e(n + 1)|) / (|e(n)|^p) = K The...
22. ### Bounded intervals in R and bisection method proof

Homework Statement Let property 1 be : If [ai,bi] is a sequence of intervals that are closed such that for each i the interval [a(i+1), b(i+1)] is either the left half of [ai,bi] or the right half, then there exists precisely 1 number in all intervals sequence. Show if a field f...
23. ### Differential equations, euler's method and bisection method

Homework Statement Hi guys, I have the following problem and I don't know how to start. I am given that W = 0.5, X(0) = 0, Iab = 20m and ha = 5m \frac{dy}{dx}=0 and \frac{dy^2}{d^2x}=\frac{W}{T}\sqrt{1 + (\frac{dy}{dx})^2} I am told to convert the 2nd order ODE to two 1st...
24. ### Solving a Problem with Bisection Method (C Program)

here is the c program for arriving at a solution using bisection method. The ouputi s going infinte..pls help ...i think it has more of syntax errors than logical errors... main() { float a,b,c,x1,x2,x,series; double d; printf("enter a,b,c and x1(pos) & x2(neg)")...
25. ### How can I fix the bisection method loop when the decimal place value is changed?

Hi, I've written code to resolve the routes of a function using the bisection method. The code works for the current route brackets (xb and xt) and for a decimal place value of 2. However when the decimal place value is changed the loop gets stuck. Code below: #include <iostream> #include...
26. ### Fortra 90 : Error in my program of bisection method

Hello, I'm having trouble with a very simple program. I want it to approximate a square root of a number R. So here is my program : For example, if you enter R as 3, a as 1, b as 2 and Tol as 0.001, it should return " d " as the square root of we were looking for, "i" as the number of...
27. ### Solving Equation with Bisection Method - Real Root Between -2*pi and 2*pi

I need to solve this equaation: (x1cos(p)+y1sin(p))^2 * (x2sin(p)-y2cos(p)) = (x1sin(p)-y1cos(p)) * (x2cos(p)+y2sin(p))^2 ; x1,x2,y1,y2 are constants The equation would have 3 roots 1 real and two imaginary I don't need imaginary roots. I am planning to use bisection...
28. ### MATLAB Finding Root of 8x^3-36x^2+54x-12=0 Using Bisection Method

Hi, Im new to Matlab, and my lecturer asked me to do his question which is: Find one root of equation 8x^3-36x^2+54x-12=0 using the bisection method. Your answer must includethe number of iterations. Ive already read the Introduction to MATLAB 7, and Numerical Methods for Engineers. And...
29. ### Show that the Bisection Method converges to

1. The function defined by f(x)=\sin(\pi*x)has zeros at every integer x. Show that when -1<a<0 and 2<b<3, the Bisection method converges to a. 0, if a+b<2 b. 2, if a+b>2 c. 1, if a+b=2 2. Bisection Method An interval [a_{n+1},b_{n+1}]containing an approximation to a root of f(x)=0 is...