- #1
kalleC
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Homework Statement
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)
Homework Equations
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)