LU Decomp in a For loop

Hello,

I am trying to write a code that decomposes matrix A to solve for vector b for 50 timesteps

I am given the b0 vector and am supposed to go from there till I reach the vector b50. Each iteration should overwtire the old vector with the new vector.

This is my code so far:

%find lower and upper of the A matrix Ax=b
% L U X  = b
% d = b/L
% U X  = d
% L d = b
[L U] = lu(A);
b0 = b;
d0 = L\b0;
x0 = U\d0
%%%%%
b1 = x0
d1 = L\b1;
x1 = U\d1
%%%%
b2 = x1
d2 = L\b2;
x2 = U\d2
%%%% and so on.....

but I want to continue this till b50

How would I be able to write this in a for loop for fifty iterations? I know that might be a basic question, but I am a beginner.

Thank you

Answer 1

[Geoff Hayes]

Layla - since your b* are really just the x*, you probably only need one 2D array for x that will store the results for each iteration. Storing all the data in one array is preferrable to storing the data in multiple variables. Try the following

x = []; % alternatively you can pre-size this if you know the number of rows of each x*
[L U] = lu(A);
x(:,1) = b;
for k = 1:51
    b = x(:, k);
    d = L\b;
    x(:, k+1)= U\d;
end

We iterate 51 times so that we calculate the x0,x1,x2,...,x50 i.e. 51 columns of x.

[Layla Bitar]

Thank you so much, this makes and sense and it really helped!