Question

study of approximation​

Answer 1

here is your answer

One of the objectives in approximation theory is the investigation of the following problem. If E is a Banach space, a linear subspace S is prescribed, whose elements s ∈ S are utilized for approximating u ∈ E. The interesting problem, known as best approximation, is to find, for a fixed u ∈ E, an element s ∈ S, for which ||u – s|| is as small as possible. To be precise, if the infimum is attained by one or more elements of S, in the relation

d(u,s)=infs∈S‖u−s‖,

then these elements of S, are called best approximations of u in S.

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