Sentence examples similar to a careful approximation. from inspiring English sources
At best they're careful approximations.
It is also shown with numerical examples that a careful selection of the approximation space to fit individual PDE and initial and boundary conditions often provides more accurate results than the DG methods based on the polynomial approximation spaces of the same order of accuracy.
Using an exact and an asymptotic solution describing the nontrivial three-dimensional fluid flow generated by a slender precessing spheroid, we present a careful analysis of the approximation of the flow using the method of regularized Stokeslets, where the regularized Stokeslets are placed along the centerline of the spheroid.
We do not yet take into account phase changes whose approximation requires a careful thermodynamic consistent procedure.
A careful error bound analysis of the Hermite approximation is given and a theoretical estimate for the optimal value of its parameters is obtained.
Clairaut showed that the approximations made by Newton and those who followed had been too rash and that with more-careful approximations, the advance of perigee came out just right.
A careful Taylor expansion indicates the second order truncation error of such a splitting approximation, and a linearized stability analysis for the numerical error function yields the desired convergence estimate in the energy norm.
Empirically, log-concavity seems to imply fast convergence of EP to a close posterior approximation, and a numerically robust behavior can be obtained in a careful implementation.
A careful analysis in these two regimes is given based upon asymptotic expansions, leading to systematic methods for rapidly finding accurate approximations.
A careful numerical analysis is performed, which points out the numerical intricacies originating from the singularity of the nuclei and the necessity for approximations in the numerical setting, with the ambition to enable solutions within a predefined accuracy.
