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On Mon, 08 Nov 2010 13:23:46 -0600, Pauli Virtanen <p...@iki.fi> wrote: > Mon, 08 Nov 2010 13:17:11 -0600, Joon wrote: >> I was wondering when it is better to store cholesky factor and use it to >> solve Ax = b, instead of storing the inverse of A. (A is a symmetric, >> positive-definite matrix.) >> >> Even in the repeated case, if I have the inverse of A (invA) stored, >> then I can solve Ax = b_i, i = 1, ... , n, by x = dot(invA, b_i). Is >> dot(invA, b_i) slower than cho_solve(cho_factor, b_i)? > > Not necessarily slower, but it contains more numerical error. > > http://www.johndcook.com/blog/2010/01/19/dont-invert-that-matrix/ > >> I heard calculating the inverse is not recommended, but my understanding >> is that numpy.linalg.inv actually solves Ax = I instead of literally >> calculating the inverse of A. It would be great if I can get some >> intuition about this. > > That's the same thing as computing the inverse matrix. > Oh I see. So I guess in invA = solve(Ax, I) and then x = dot(invA, b) case, there are more places where numerical errors occur, than just x = solve(Ax, b) case. Thank you, Joon -- |
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