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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
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