To use the bisection method to solve the roots of an equation, you can follow these steps:
Define a function to calculate the value of the equation. Assuming that the equation we want to solve is f(x)=0, then this function can be written in the form of def f(x):.
Determine the search range of dichotomy. Based on the properties of the equation, choose a left boundary and a right boundary such that f (left boundary) and f (right boundary) have opposite signs. That is, if f(left boundary) is positive and f(right boundary) is negative, or f(left boundary) is negative and f(right boundary) is positive.
Iterate over the search range using the bisection method until the roots of the equation are found. Specific steps are as follows: a. Calculate the midpoint of the search range mid=(left boundary right boundary)/2. b. Calculate the value of f(mid). c. Determine the symbol of f(mid) and update the search range:
The following is a sample code that uses the bisection method to solve the roots of an equation:
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In the above code, we define an equation f(x)=x^2-4 and use the bisection method to solve the root of the equation. In the while loop, we continuously update the left and right boundaries of the search range until we find the root of the equation. Finally, the value of the root is output.
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