Abstract
Error estimates (as opposed to bounds) may involve unspecified constants, in which case they have no direct value for numerical purposes. A practical method for obtaining realistic upper bounds of such generic constants is devised here. Directly applicable as it stands to a wide class of pointwise approximation problems, this method can further be adapted technically to that alternative class of important problems which is concerned with mean-square approximation. It is based on an explicitly motivated analysis of the general problem of bounding errors, which essentially evolves in the setting of operator theory while referring to such classical tools as the Peano kernel theorem and its generalization known as the Bramble-Hilbert lemma.
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