Sentence examples for approximation out from inspiring English sources

Let f be an arbitrary element in H. Since Y is a finite dimensional and closed subspace, it is a complete subset of H. Therefore, f has the unique best approximation out of Y, such that ( y_{0} ) exists y_{0} in Y; forall y in Y: left| {f - y_{0} } right|_{2} le left| {f - y} right|_{2}.

The precise choice of derivative approximation turns out to be crucial.

Many would defend utility theory (as well as other aspects of their standard model of behaviour) as a useful approximation, pointing out that exceptions to approximations can always be found.

The basis for his statistical mathematics came from a long tradition of work on the method of least squares approximation, worked out early in the 19th century in order to estimate quantities from repeated astronomical and geodetic measures using probability theory.

That is why the Yosida approximation turned out to be more effective in this scenario, because the Yosida approximation (1.21).

Nevertheless, such the rough approximation turns out to be quite correct and sufficient to describe the general trend in behavior of as a function of r.

In practice, using a linear approximation turned out to lead to sufficiently accurate results for all incorporated methods (see Section 3.5).

This Born approximation turns out to be leading order not only in V but also, for V fixed, as (k rightarrow infty ).

This is required in the case of broad-peaked or multi-modal posterior distribution of the hyperparameters where the point approximations turn out to be insufficient.

where, obviously, for the outage probability we can use the exact formula, Pout (given by (8)), or one of its approximations, P out,A ( app ) or P out,B ( app ).

Therefore, the models presented here tend to be first-order approximations leaving out many facets of the cells' nonlinear behavior.