Looking to write a code which utilises a formula to solve an equation

clc

clear all

close all

AF = @(x) x^3-4x^2-1; % function equation

xR(R/2) = 46/x + 5(x-3); % iterative formula

x3 = 1;

Very new to MATLAB and was wondering how I would go about creating an iteration to output solutions to the problem.

[Mehmed Saad]

1. what is xRk
2. For how many iterations of R you want to run the formula
3. what is the purpose of AF function in this code?

[Sinclair Song]

1. My mistake, it's just meant to be xR, I've corrected it now

2. I'd say 100 to get possible solutions

3. AF is the function equation I'm trying to solve using the values generated from the iterative equation

Answer 1

[Mehmed Saad]

k=100;
xR = zeros(1,k);
xR(1) =2; % Initial Guess
for i=2:k
xR(i) = 1+ (1/xR(i-1)); % iterative formula 
end

Now xR is an array which contains the value for 100 iteration where each iteration value depends on previous one

[Sinclair Song]

Thank you for the response, I tried fitting your answer into the code but I don't seem to be receiving an output. Would an additional 'while' loop be required in order to fit in the desired error limit?

[Mehmed Saad]

err = 1;
x0 =2; % Initial Guess
while(err>0.05)
xR = 1+ (1/x0); % iterative formula 
err = abs(xR-x0);
x0 = xR;
end

[Sinclair Song]

Could I ask why the err was intiated with 1? The script isn't returning any errors nor any outputs.

[Mehmed Saad]

i just initialized the err with 1, so that when while loop runs, it first check the condition, if err is not initilized then it will give error (undefined variable err) so we defined an initial value of variable err

write err in cmd

err

or just type err after the while loop end

You can see err in your workspace, it is less than 0.05.

If you want all the xR values, try indexing the array.

[Sinclair Song]

Oh so it turns out the solution is too small to pick up, if I'm interpretting that correctly? How would I go about indexing an array? Thanks for all the guidance!

[Mehmed Saad]

Try using matlab help and google

in this way you can learn matlab faster