1. Limited time only! Sign up for a free 30min personal 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!

Cholesky Factorization Proofs

  1. Oct 15, 2011 #1
    1. The problem statement, all variables and given/known data
    Let A =[A11 A12; A*12 A22] be Hermitian Positive-definite.
    Use Cholesky factorizations
    A11 = L1L*1
    A22 = L2L*2
    A22-A*12 A-111 A12 = L3L*3

    to show the following:

    ||A22-A*12 A-111 A12||2≤||A||2

    2. Relevant equations



    3. The attempt at a solution

    Using the submultiplicative and triangle inequalities:

    ||A22||2+||A*12||2 ||A-111||2||A12||2≤||A||2
     
  2. jcsd
  3. Oct 18, 2011 #2
    Can anyone help?
     
Know someone interested in this topic? Share this thread via Reddit, Google+, Twitter, or Facebook




Similar Discussions: Cholesky Factorization Proofs
Loading...