# Mastering Newton's Method and Graphing in Matlab: A Step-by-Step Tutorial

• MATLAB
• twoski

#### twoski

Hey guys, I have to make some graphs for an assignment and a friend told me it would be easiest with matlab.

I need to make an x(k+1) vs. x(k) graph for Newton's method as well as the Chord method. I also need to make a few charts of the discrete logistic equation.

Plotting functions isn't what confuses me, it's making the line that depicts the iteration which gets me.

Any examples or tutorials would be appreciated.

What have you tried so far? Can you show some of your code that you've been working on?

Vague descriptions usually don't go too far in forums.

## 1. What is Newton's Method and why is it important?

Newton's Method is a mathematical algorithm used to find the roots of a given function. It is important because it allows us to solve complex equations that may not have an analytical solution, and it is also a fundamental tool in numerical analysis and optimization.

## 2. How can I use Matlab to implement Newton's Method?

To implement Newton's Method in Matlab, you can use the built-in function fzero which takes in the function and an initial guess as inputs. Alternatively, you can write your own code using a loop structure to iteratively update the guess until the root is found.

## 3. Can I use Newton's Method for any type of function?

Yes, Newton's Method can be used for any type of function as long as it is continuous and differentiable. However, the method may fail to converge if the function has multiple roots or if the initial guess is too far from the root.

## 4. How do I know if Newton's Method has converged to the root?

You can check for convergence by setting a tolerance value and comparing the difference between consecutive guesses to this tolerance. If the difference is smaller than the tolerance, then the root has been found. Additionally, you can plot the function and visually check if the algorithm is converging to the root.

## 5. Is it possible to graph the function and the iterations of Newton's Method in Matlab?

Yes, you can use the plot function in Matlab to graph the function and the iterations of Newton's Method. You can also use the hold function to plot the iterations on top of the function plot. This can be useful for visualizing the convergence of the algorithm.