Loop does not work

format long

tolerance = 10^-15;

y=0.1;

h=[y,y/2,y/4,y/8,y/16];

x=0;

I = (exp(x+h)-exp(x))./h;

z = length(h);

for n = 1:z-1 ;

while m < z-n

I(m) = (4/3) * I(m+1) - (1/3) * I(m);

m = m+1;

end

end

I

This is the code and i expected that the I matrix should go into the loop several times and as a result I should see 1x1 matrix but the loop stops after first iteration. What could be the problem?

[Dyuman Joshi]

m is not defined in the code above.

Please specify

> why I should be 1x1.

> what is the objective here / what you are trying to do.

[Torsten]

Is this Richardson extrapolation ? Or what are you trying to do in your code ?

Shouldn't I be a lower triangular matrix in this case instead of a vector ?

[Torsten]

If I is a matrix, then why do you work with it as a vector ?

Answer 1

[Hassaan]

You haven't initialized m before the loop starts, and you're using it as a loop index. This can lead to unexpected behavior or errors. Furthermore, your while loop condition m < z-n might not be behaving as expected, especially if m is not properly initialized and updated. Here's are some suggestions:

1. Initialize m: Before entering the while loop, you should initialize m to a starting value. Typically, for MATLAB indexing, you would start with m = 1.
2. Reset m in each iteration: You need to reset the value of m for each iteration of your n loop. If you don't reset it, m will eventually exceed z-n, and the inner loop won't run in subsequent iterations of the outer loop.
3. Adjust the loop conditions: Ensure that the loop runs as many times as you expect and that the indices used inside the loop do not exceed the dimensions of your I array.

format long
tolerance = 10^-15;
y = 0.1;
h = [y, y/2, y/4, y/8, y/16];
x = 0;
I = (exp(x + h) - exp(x)) ./ h;
z = length(h);

for n = 1:(z-1)
    m = 1;  % Initialize m at the beginning of each n loop
    while m <= (z - n)  % Ensure m doesn't exceed the updated length of I
        I(m) = (4/3) * I(m + 1) - (1/3) * I(m);
        m = m + 1;
    end
    I = I(1:end-1);  % After updating I, truncate the last element
end

disp(I)

   1.000617319458443

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If you find the solution helpful and it resolves your issue, it would be greatly appreciated if you could accept the answer. Also, leaving an upvote and a comment are also wonderful ways to provide feedback.

[Mehmet]

thank you for answering. but i couldn't understand that why the truncation of the matrix made it work?