root finding problem in matlab

To solve root finding problems in Matlab, you can use a variety of numerical methods, such as the bisection method, the secant method, or Newton's method. In this example, I will demonstrate how to find the root of a function using the bisection method.

Here is an example code:

main.m
% Define the function to find the root of
f = @(x) x^2 - 4;

% Define the initial brackets for the bisection method to search through
a = 0;
b = 3;

% Set a tolerance level for the error between iterations
tol = 1e-6;

% Keep track of the number of iterations it takes to converge
n = 0;

% Use the bisection method to find the root of the function
while abs(b-a) > tol
    mid = (a + b)/2;
    if f(mid) == 0
        break
    elseif f(mid)*f(a) < 0
        b = mid;
    else
        a = mid;
    end
    n = n + 1;
end

% Print the result
fprintf('The root is %f, found in %d iterations', mid, n);
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In this code, we define our function to find the root of as f, then set our initial brackets for the bisection method as a and b. We also define a tolerance level for the error between iterations tol, and set our iteration counter n to 0.

We then enter a while loop, where we calculate the midpoint mid between a and b. If the function f evaluated at mid is 0, we have found the root and break the loop. If f evaluated at mid times f evaluated at a is less than 0, we know the root is in the left half of the brackets, so we update b to mid. Otherwise, we know the root is in the right half of the brackets, so we update a to mid.

We continue iterating until the difference between b and a is less than our tolerance level. At this point, we have found our root, and print it out along with the number of iterations it took to converge.

This is just one example of how to solve root finding problems in Matlab. Depending on your needs, other numerical methods may be more appropriate.