Sentence examples for proof of approximation from inspiring English sources

The algorithm proposed in this paper was given without any proof of approximation quality, only indicating the extreme circumstances of problem instance.

In [16], the authors give the proof of approximation when the X i,j is i.i.d with the Markov Chain imbeddable systems [17].

We give a short proof of the Approximation Conjecture with complex coefficients for amenable groups [G. Elek, The Strong Approximation Conjecture holds for amenable groups, J. Funct. Anal. 239 (1) (2396) 345–355].

The rigorous proof of universal approximation of extreme learning machine with much milder conditions makes it a preferable choice in many different approaches.

To him is owed the first appearance and proof of the approximation 31/7 for the ratio of the circumference to the diameter of the circle (what is now designated π).

We only give the proof of the approximation order.

The first constructive (and simple) proof of Weierstrass approximation theorem was given by Bernstein [1].

For a proof of the approximation of the Čech complex by the VR complex, see [80]; see [97] for a generalization of this result.

Originally introduced by Sergei Natanovich Bernstein to facilitate a constructive proof of the Weierstrass approximation theorem, the leisurely convergence rate of Bernstein polynomial approximations to continuous functions caused them to languish in obscurity, pending the advent of digital computers.

The following fixed-point theorem is fundamental for the proof of the best approximation theorem.

For a real-valued bounded function f on ([0,1]), Bernstein [2] defined a sequence of polynomials given by begin{aligned} B_{n}(f;x)=sum_{r=0}^{n}f biggl( frac{r}{n} biggr) {binom{n}{r}}x^{r} 1-x ^{n-r}, quad forall xin [0,1]mbox{ and } 1-x ^{n-r}{N} 1-x ^{n-r}ed} to provide a very simple and elegant proof of the Weierstrass approximation theorem.