Combining Functions of Gaussian elimination and Banded Matrix

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Hmm! 2021-2-8

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编辑： Hmm! 2021-2-8

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Goal: to create a banded version of Gaussian elimination without pivoting.

%%Work so far: I have a code that generates a banded matrix. . .

function [Z]=bandmatrix(n,k1,k2)

Z=zeros(n,n);
for i=1:n
    for j=1:n
        Z(i,j)=1;
    end
end
for i=1:n
    for j=1:n
        if (j<i-k1) Z(i,j)=0;
        end
        if(j>i+k2) Z(i,j)=0;
        end
    end
end

%% I have a code for GE without pivoting as. . .

function [x] = GE_WithoutPivoting1(A,b)
n = length(b);
for k=1:n-1
    if abs(A(k,k)) < 1e-15
        error('A has diagonal entries of zero')
    end    
for i=k+1:n
        m = -A(i,k)/A(k,k); % multiplier for current row i
        for j=k+1:n
            A(i,j) = A(i,j) + m*A(k,j);
        end
        b(i) = b(i) + m*b(k); 
    end
end
x = GE_BackSubstitution(A,b);

QUESTION: to achieve my goal as in above, i.e., to properly implement a banded version of Gaussian elimination without pivoting. What I did was to call the GE elimination at end of the function [Z]=bandmatrix(n,k1,k2) i.e.,

function [Z]=bandmatrix(n,k1,k2)
....
....
x = GE_BackSubstitution(A,b); %This is already in my working directory

But my fear is that function [Z]=bandmatrix(n,k1,k2) might not be working and that it is function [x] = GE_WithoutPivoting1(A,b) that is working (since it is already saved on my working directory).

Please, using my two functions how do I implement a banded version of GE without pivoting. Any edition to my written codes will be welcome. Thank you