Performing Gauss Elimination with MatLab
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K =
-0.2106 0.4656 -0.4531 0.7106
-0.6018 0.2421 -0.8383 1.3634
0.0773 -0.5600 0.4168 -0.2733
0.7945 1.0603 1.5393 0.0098
I have the above matrix and I'd like to perform Gauss elimination on it with MatLab such that I am left with an upper triangular matrix. Please how can I proceed?
답변 (3개)
József Szabó
2020년 1월 29일
function x = solveGauss(A,b)
s = length(A);
for j = 1:(s-1)
for i = s:-1:j+1
m = A(i,j)/A(j,j);
A(i,:) = A(i,:) - m*A(j,:);
b(i) = b(i) - m*b(j);
end
end
x = zeros(s,1);
x(s) = b(s)/A(s,s);
for i = s-1:-1:1
sum = 0;
for j = s:-1:i+1
sum = sum + A(i,j)*x(j);
end
x(i) = (b(i)- sum)/A(i,i);
end
댓글 수: 2
Tyvaughn Holness
2020년 3월 28일
편집: Tyvaughn Holness
2020년 3월 29일
Great work, thanks! I found a faster implementation that avoids the double for loop to reduce complexity and time.
Richard Brown
2012년 7월 12일
The function you want is LU
[L, U] = lu(K);
The upper triangular matrix resulting from Gaussian elimination with partial pivoting is U. L is a permuted lower triangular matrix. If you're using it to solve equations K*x = b, then you can do
x = U \ (L \ b);
or if you only have one right hand side, you can save a bit of effort and let MATLAB do it:
x = K \ b;
댓글 수: 2
Richard Brown
2012년 7월 13일
I wouldn't expect it would necessarily compare with published literature - what you get depends on the pivoting strategy (as you point out).
Complete pivoting is rarely used - it is pretty universally recognised that there is no practical advantage to using it over partial pivoting, and there is significantly more implementation overhead. So I would question whether results you've found in the literature use complete pivoting, unless it was a paper studying pivoting strategies.
What you might want is the LU factorisation with no pivoting. You can trick lu into providing this by using the sparse version of the algorithm with a pivoting threshold of zero:
[L, U] = lu(sparse(K),0);
% L = full(L); U = full(U); %optionally
James Tursa
2012년 7월 11일
You could start with this FEX submission:
댓글 수: 2
James Tursa
2012년 7월 13일
You need to download the gecp function from the FEX link I posted above, and then put the file gecp.m somewhere on the MATLAB path.
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