# Solve a nonlinear equation using fixed-point iteration in MATLAB

• Fatima Hasan
In summary, in order to plot the function g(x), the individual should first define the values of x and g, and then calculate the fixed-point. The code should include a hold on function and end with a plot of x and fixed_g. Additionally, there may have been an error in the code as indicated by the last two statements.
Fatima Hasan
Homework Statement
The statement is attached below.
Relevant Equations
-
My attempt is attached below.
When I tried to solve it , nothing comes up. However, there are no errors !

You are plotting just one point at the end, with coordinates (maxiter + 1, x(maxiter + 1)).

If you want to plot ##g(x)##, you should do something like this (for example before calculating the fixed-point):
Matlab:
x= -10:0.01:10;
g = x^5-3*x^3-2*x^2+2;
plot(x, g);

After this, you should calculate the fixed-point. If you call it ##x## in your code, you can do the following after the fixed-point iteration:
Matlab:
hold on;
fixed_g = x^5-3*x^3-2*x^2+2;
plot(x, fixed_g, 'o');

Jaime_mc2 said:
g = x^5-3*x^3-2*x^2+2;
I got an error .

Jaime_mc2 said:
g = x^5-3*x^3-2*x^2+2;
I got an error .

## 1. What is fixed-point iteration?

Fixed-point iteration is a numerical method used to find the roots of a nonlinear equation. It involves repeatedly applying a function to an initial guess until the resulting value is within a desired tolerance of the true solution.

## 2. How does fixed-point iteration work in MATLAB?

In MATLAB, fixed-point iteration can be implemented using a while loop that checks for convergence based on a specified tolerance. The function being iterated can be defined as a separate function or as an anonymous function within the loop.

## 3. What are the advantages of using fixed-point iteration in MATLAB?

Fixed-point iteration is a simple and easy-to-understand method for solving nonlinear equations. It also allows for a high degree of control over the convergence criteria and can handle a wide range of functions.

## 4. Are there any limitations to using fixed-point iteration in MATLAB?

Fixed-point iteration can be slow to converge for certain functions, and it may not converge at all if the initial guess is too far from the true solution. It also requires the function to be continuously differentiable.

## 5. How can I improve the convergence of fixed-point iteration in MATLAB?

There are several techniques that can be used to improve the convergence of fixed-point iteration, such as using a different initial guess, modifying the function being iterated, or using a different convergence criteria. It may also be helpful to plot the function to get a better understanding of the behavior near the root.

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