Let a u v the solution is x 1 vnk 1 k vn where

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Unformatted text preview: ν = A − Aν F = ν i =1 σi ui vi min = rank(B )≤ν , 2 2 σν +1 + · · · + σr 12 / 20 Sensitivity of square systems If n A= σi ui vi = U ΣV i =1 is the SVD of A, then n −1 x=A b = (U ΣV ) −1 b= i =1 ui b vi σi Small changes in A or b can induce relatively large changes in x if σn is small The magnitude of σn has bearing on the sensitivity of the Ax = b problem The solution x is increasingly sensitive to perturbations 13 / 20 Condition Consider the parameterized system (A + εF )x(ε)...
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