It is well known that the approximation error of the SVD is(adsbygoogle = window.adsbygoogle || []).push({});

[itex]\left\| \textbf{A}-\textbf{A}_{\rm SVD} \right\| = σ_k[/itex],

where [itex] σ_k[/itex], is thek-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]?

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# SVD approximation error

Can you offer guidance or do you also need help?

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