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Approximation theory is concerned with how functions can best be approximated with simpler functions, and with quantitatively characterizing the errors introduced thereby.

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Literature Request: Finite Dimensional "Approximations" of Linear Operators

A canonical reference is : Spectral Approximation of Linear Operators by Chatelin. http://epubs.siam.org/doi/book/10.1137/1.9781611970678
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