Sentence examples for proven approximation from inspiring English sources

This creates a wide scope for developing approximation methods and algorithms that are able to produce solutions with proven approximation guarantees.

We also prove approximation results for such vector fields: the dense sets are formed either by unit-length divergence-free vector fields that are smooth except at a finite number of points and the approximation result holds in the W1,qloc-topology (1⩽q<2), or by everywhere smooth unit-length vector fields (not necessarily divergence-free) and the approximation result holds in a weaker topology.

In [12], Wan et al. proved the approximation ratio of [7] is 7.333 and proposed a new approximation algorithm with ratio 6.389.

As an application we prove nonmonotone approximation theorems for Schrödinger operators with singular magnetic fields and singular complex potentials.

We now prove the approximation factor.

In the present paper, we prove new approximation properties of ((p,q -analog of Bernstein operators.

We also prove several approximation results and successfully extend the results of [19].

In this paper, we prove an approximation theorem for equilibrium problems and provide theoretical support for many algorithms.

In this paper, we construct a new family of operators, prove some approximation results in A-statistical sense and establish some direct theorems for Kantorovich-type integral operators.

In [5], the idea of statistical σ-convergence is defined which is further applied to prove some approximation theorems in [6] and [7].

Experiments are performed on four datasets, and experimental results prove that approximation coefficients are efficient way to characterize the microarray data.