Algorithm to extract linearly dependent columns in a large scale [-1,1] matrix ( 10^5 by 10^6)
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I am trying to find an efficient algorithm for extracting linear independent collumns ( an old problem) but on a Very large matrix ( 10^5 rows, 10^6 columns) with all +-1 Real elements.... so , a dense matrix.
these matrcies are so large that I have no hope to put them in memory all at once, and then use the standard QR algorithm (or other real matrix decompositions that I have found) .
I know the choice of spanning collumns are not unique. I just want a subset "Q" of N colums of the Matrix A, such that rank(A) = N = rank(Q)
I have been looking for a clever random algorithm with bounded error.