# Looking for simple iteration method

• dmehling
In summary, the conversation discusses the need for an easy way to perform simple iterations using the equation z^2 + c. The desired output is in tabular form and the use of a spreadsheet is suggested. The conversation also mentions the possibility of using the Mandelbrot set and provides a basic idea for implementing the desired iterations. The idea involves setting an initial value for z and using a loop to continuously evaluate z^2 + c and store the value in z until a certain condition is met. The person requesting help mentions their lack of programming experience and asks for the easiest way to implement this.
dmehling
I'm looking for an easy way to perform simple iterations. For example using the equation: z^2 + c, although I don't need it to do complex numbers. Also, I would like the iterations to be listed in tabular form.

It isn't very clear what you are asking. Iterations to do what? Solve f(x) = 0 by iteration?? Something like Newton's method? If you want results in a tabular form a spreadsheet might be just the ticket.

I think you might be the same person who asked about the Mandelbrot set. What you want to do is this

Set c.
1. Set z with an initial value.
2. Evaluate z^2 + c.
3. Store the value of the previous step in z.
4. Go to step 2.
This is the basic idea, but it is oversimplified, and is an infinite loop. What you are doing is getting a sequence z0, z1, z2, ...To keep the loop from iterating forever, you want to exit the loop when |z| gets above a certain size. It's been a while since I looked at any Mandelbrot algorithms, but maybe the cutoff is |z| >= 2.

Hope this helps.

Yes, that is what I need to do. However, I'm not sure how I would actually implement this. I have no real experience in programming. I am looking for the easiest way of doing it.

## 1. What is the simple iteration method?

The simple iteration method, also known as the fixed-point iteration method, is an algorithm used to find the root of a function. It involves repeatedly applying a function to an initial guess until a desired level of accuracy is achieved.

## 2. How does the simple iteration method work?

The simple iteration method works by starting with an initial guess, plugging it into the function, and then using that output as the next guess. This process is repeated until the difference between consecutive guesses is within a desired tolerance level.

## 3. What are the advantages of using the simple iteration method?

The simple iteration method is relatively easy to implement and requires minimal mathematical knowledge. It can also be used to find roots of complex functions that cannot be solved algebraically.

## 4. What are the limitations of the simple iteration method?

The simple iteration method can only find a root if the function is continuous and the initial guess is close enough to the actual root. It may also converge slowly or not converge at all for certain functions.

## 5. Can the simple iteration method be used for optimization problems?

Yes, the simple iteration method can be adapted for optimization problems by finding the minimum or maximum of a function instead of its root. However, it may not be the most efficient method for optimization and other algorithms may be more suitable.

Replies
19
Views
1K
Replies
1
Views
9K
Replies
9
Views
2K
Replies
1
Views
953
Replies
1
Views
10K
Replies
1
Views
879
Replies
1
Views
10K
Replies
4
Views
1K
Replies
3
Views
2K
Replies
10
Views
3K