QUESTION: How would I go about generating a d block diagonal system for d = [ 5,10,15....50] and solve each system by integrating the two functions above.

FIRST Function for Gauss elimination:

function [x, A, b] = GE(A, b)

%-------------------------------------------------------------------------%

%GaussE: Function which performs Gauss Elimination, pivoting if required.

%INPUTS

% A = Input A matrix

% b = Input b vector

%OUTPUTS

% A = The forward eliminated coefficient matrix

% b = The forward eliminated b vector

% x = The final solution vector x

%-------------------------------------------------------------------------%

n = length(A);

%-------------------------------------------------------------------------%

% FORWARD ELIMINATION START:

%-------------------------------------------------------------------------%

for i = 1:(n-1) % Pivot row index (stop at 2nd last row)

%-------------------------------------------------------------------------%

% < INSERT PARTIAL PIVOTING CODE HERE >

%-------------------------------------------------------------------------%

for k = (i+1):n % Skips the pivot element and indexes what is BELOW it in the SAME COLUMN as the pivot element.

factor = ( A(k,i) / A(i,i) ); % Calculates the row factor for current row

for j = 1:n % Column index

A(k,j) = A(k,j) - factor*A(i,j); % Row subtraction, element-by-element

end

b(k) = b(k) - factor*b(i); % Updates b

end

end

%-------------------------------------------------------------------------%

% FORWARD ELIMINATION END

%-------------------------------------------------------------------------%

%-------------------------------------------------------------------------%

% BACKWARDS SUBSTITUTION START:

%-------------------------------------------------------------------------%

x = zeros(n,1);

x(n) = b(n) / A(n,n); % Compute x(n) immediately

for i = (n-1):(-1):(1) % Row index, starting at the 2nd last row and working backwards

summ = b(i);

for j = (i+1):n % Before solving for x(i), need to subtract all terms to the RIGHT of the current pivot element (if any).

summ = summ - A(i,j)*x(j);

end

x(i) = summ/A(i,i); % Divide final 'sum' by the pivot element

x

end

%-------------------------------------------------------------------------%

% BACKWARDS SUBSTITUTION END

%-------------------------------------------------------------------------%

end

Second function:

function [x]=BlockDiagonalSolver(A,b)

n=length(A);

d=sqrt(length(A));

x=zeros(n,1);

for i= 1:d

start_row=((i-1)*d+1);

end_row=(i*d);

h=start_row:end_row;

A_solve=A(h,h);

b_solve=b(h);

[A_1,b_1,x(h)]= GaussE(A_solve,b_solve);

end