Sentence examples for remainder estimates from inspiring English sources

We give optimal remainder estimates for the rate of clustering of eigenvalues.

While they also rely on the representation formula from [3] they require an inductive procedure and careful remainder estimates.

Consequently, we obtain the strong convergence of to, and the remainder estimates now follow from Lemma 2.6.

Then the remainder estimates could be improved to (O(h^{-d+1+nu }|log h|^{-1-nu })) or even to (O(h^{-d+1+nu +delta })) respectively.

Then one can prove easily that the standard conditions to the trajectories are fulfilled and we may use the improved remainder estimates.

The variational method was developed further by many mathematicians, but it lead to generalizations rather than to getting sharp remainder estimates and we postpone its discussion until Sect.

Moreover, under the non-periodicity condition, the remainder estimate is "o".  .

Furthermore,  if Open image in new window then the remainder estimate is O(1).

To improve this remainder estimate, we should carefully study the propagation of singularities.

For (d=3), we cannot expect a remainder estimate better than (O(h^{-1})).

(ii) Furthermore,  if Open image in new window then the remainder estimate is O(1).