What is the algorithm for LU factorization in MATLAB, i.e. [L,U] = lu(a)?
After searching for many examples and trying to compare the result with MATLAB,
they are all different.
However, I would like to do the result as it is in MATLAB. Which books contain the algorithm; or, what is exact algorithm used?
a = [1,2,3;4,5,6;7,8,9]
[L,U] = lu(a)
I Googled this, and it is different from MATLAB:
http://web.mit.edu/18.06/www/Course-Info/Tcodes.html
http://www.stat.nctu.edu.tw/~misg/SUmmer_Course/C_language/Ch06/LUdecomposition.htm
Best Answer
Nothing special here. MATLAB just uses a type of row exchange algorithm, of which the pivot element is selected. The default threshold of selecting is 1, as mentioned in MATLAB's help document. Try [L,U,P] = lu(a), where P shows the row permutation of the matrix a, based on the pivot selecting criteria A(i,j) >= thresh(1) * max(abs(A(j:m,j))).