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!

Homework Help: Condition number of a matrix

  1. Sep 25, 2009 #1
    1. The problem statement, all variables and given/known data
    For a system of equations Ax = b
    Let dA be a random perturbation of the matrix A

    The error in

    Which dA fullfills the equality

    norm(A^-1 (da) x) = norm(A^-1) norm(dA) norm(x)

    (The SVD of A is known)
    (b is a known vector)

    2. Relevant equations

    3. The attempt at a solution
    I managed to solve a somewhat similar question asking for what b and db fullfills the upper bound for K = norm(A)*norm(b)/norm(x) <= cond(A)

    when b = A*V(:,1) and db = U(:,5) <-- clearly rows and columns values corresponding to the smallest singular value of A

    However for this particular question I am clueless as to how to form dA to maximise the condition number so it reaches cond(A) = norm(A)*norm(A^-1)
  2. jcsd
Share this great discussion with others via Reddit, Google+, Twitter, or Facebook

Can you offer guidance or do you also need help?
Draft saved Draft deleted