Le 05/02/2024 à 11:30, Dima Pasechnik a écrit :
A good implementation of LU decomposition ought actually to take non-square matrix as input, and have the indices adjusted appropriately in the algorithm, so it's indeed a bit strange that superLU only takes square matrices (?). Perhaps it's a good idea to look at its docs and the source code.
Actually, SuperLU whas developed for people (like me) who solve discretized Partial Differential Equations. In that case, matrices are quite always square matrices. It is an old program. The idea whas that given the fact that new non zero terms appear during the LU-factorization, but that we can predict where they appear and minimize the amount of these news terms, there exists a class of rather large problems (but not too large! -say less than 10^6 unknowns-) for which a direct method, efficiently coded, could be faster than an iterative one (and this is true).
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