How can I use LU factorization in the most memory saving way?

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Amos 2015-1-9

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https://ww2.mathworks.cn/matlabcentral/answers/169365-how-can-i-use-lu-factorization-in-the-most-memory-saving-way

Hello,

I would like to solve linear equations of the form Ax=b by means of LU decomposition. As the solution is seeked for several right hand side vectors b, I would like to store the decomposition of A such that it can be reused.

As the matrix A is very big, the otherwise very usefull package "factorize" from file exchange causes problems, as it returns a structure containing A, L and U as full matrices, which don't fit into the memory together.

The Matlab function lu can be called in a way that the L and U matrices are put together into one matrix Y = lu(A) with Y = U+L-eye(size(A)). This way, only A and one other matrix of the same size need to fit into the memory. However, in this case the permutation matrix P is not returned and I don't know how I can solve for x without it.

Do you have a suggestion how I can resolve this problem?

Thanks in advance, Amos