1. Not finding help here? Sign up for a free 30min tutor trial with Chegg Tutors
    Dismiss Notice
Dismiss Notice
Join Physics Forums Today!
The friendliest, high quality science and math community on the planet! Everyone who loves science is here!

Numerical LA: Cholesky & Conjugate gradient method

  1. Feb 15, 2005 #1

    I have to do a proof and am having trouble starting.

    The proof is to show how you could use Cholesky decomposition to determine a set of A-orthogonal directions.

    Cholesky decom. means I can write the symmetric positive definite matrix as

    A = GG'

    The textbook gives a way of determining the A-orthogonal set using A. Specifically,

    v_k = r_k-1 + s_k-1*v_k-1

    where v_k is the kth direction vector and r_k-1 is the k-1 residual vector. So we want to choose s_k-1 such that

    <v_k-1, Av_k> = 0

    The textbook then goes onto show:

    s_k-1 = - <v_k-1, Ar_k-1> / <v_k-1, Av_k-1>

    So I don't see how using A = GG' helps at all.

    If anyone could give me a tip on how to start, I'd be thankful.
  2. jcsd
Know someone interested in this topic? Share this thread via Reddit, Google+, Twitter, or Facebook

Can you help with the solution or looking for help too?
Draft saved Draft deleted

Similar Discussions: Numerical LA: Cholesky & Conjugate gradient method
  1. Choleski Split (Replies: 1)