Sentence examples for bounds for the approximation from inspiring English sources

In the third section, we use the operator method from [4] to establish the bounds for the approximation of Poisson-binomial distribution by Poisson distribution.

We provide suitable error bounds for the approximation of bandlimited functions by linear combinations of certain special functions the prolate spheroidal wave functions of order 0. The coefficients in the approximating linear combinations are given explicitly via appropriate quadrature formulae.

Bounds for the approximation error to the NBL were given by Dümbgen and Leuenberger [26] for the (half- normal, thalf- normall, the Gumbel, and the Weibull (including the exponential) distributions.

We derive Chen Stein error bounds for the approximation.

Iyengar proved a useful inequality which gives an upper bound for the approximation of the integral average by the mean of the values of mapping at end points of the interval that is given below (see [7] or [11, p.471]).

This inequality gives an upper bound for the approximation of the integral average 1 b − a ∫ a b f ( t ) d t by the value f at a point x ∈ ( a, b ).

In Sects.  4 and  5, we introduce a general analytical framework of nonlinear evolutionary variational inequalities and its fully discrete counterpart; in particular, we deduce a result on the existence and uniqueness of the fully discrete solution as well as a priori bounds for the discrete approximation values.

Based on results of the Kolmogorov n-width theory the paper provides useful bounds for the worst case approximation error - both H2 and H∞ – in terms of the hyperbolic distance related to the sets of uncertain poles.

It is difficult to give the upper bound for the abstract approximation error.

The following theorem then gives an upper bound for the best approximation error of Theorem 1: Assume the exact solution of (3 -(4) is such that (mathbf {A} in mathbf {H}(mathbf {curl},Omega ) cap H^{s}({Omega_{1}, Omega_{2}})^{3}), (nablatimes mathbf {A} in H^{s}({Omega_{1}, Omega_{2}})^{3}) with integer (1 leq s leq k).

Under some regularity conditions, we obtain sharp bounds for the minimal errors for approximation and upper bounds for the minimal errors for integration.