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SVD approximation error

  1. Jul 1, 2013 #1
    It is well known that the approximation error of the SVD is
    [itex]\left\| \textbf{A}-\textbf{A}_{\rm SVD} \right\| = σ_k[/itex],
    where [itex] σ_k[/itex], is the k-th greatest singular value of matrix Ʃ in the SVD.

    Yes this tells nothing about the accuracy of the approximation.
    E.g. is it [itex] 10^{-3}, 10^{-6}, 0.1, >1?[/itex].

    I need to solve a system of equations [itex] \textbf{A}x =b[/itex] and I want to estimate the approximation error ε
    [itex]\left\| \textbf{A}-\tilde{\textbf{A}} \right\| = \epsilon[/itex],
    introduced by several different methods.

    How is ε related with the rank k of matrix instead of the obscure [itex] σ_k[/itex]?
  2. jcsd
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