[Numpy-discussion] Solving Ax = b: inverse vs cholesky factorization

Joon groups.and.lists@gmail....
Mon Nov 8 13:17:11 CST 2010


Hi,

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)?

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.

Thank you,
Joon
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