Hi @Hmm!
To create a banded version of Gaussian elimination without pivoting, you need to ensure that your Gaussian elimination function works specifically with the banded matrix generated by your "bandmatrix" function.
- Generate the banded matrix using your "bandmatrix" function.
- Apply Gaussian elimination on this banded matrix without pivoting.
Here's how you can do it:
function [Z] = bandmatrix(n, k1, k2)
Z = zeros(n, n);
for i = 1:n
for j = 1:n
if (j >= i - k1) && (j <= i + k2)
Z(i, j) = rand();
end
end
end
for i = 1:n
if abs(Z(i, i)) < 1e-15
Z(i, i) = 1;
end
end
end
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);
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);
end
% Function for back substitution
function [x] = GE_BackSubstitution(A, b)
n = length(b);
x = zeros(n, 1);
for i = n:-1:1
x(i) = (b(i) - A(i, i+1:n) * x(i+1:n)) / A(i, i);
end
end
% integrate both banded matrix generation and GE
function [x] = banded_GE(n, k1, k2, b)
A = bandmatrix(n, k1, k2);
x = GE_WithoutPivoting1(A, b);
end
n = 5; % Size of the matrix
k1 = 1; % Lower bandwidth
k2 = 1; % Upper bandwidth
b = rand(n, 1);
x = banded_GE(n, k1, k2, b);
disp(x);
Hope this helps!
