Sentence examples for a linear convergence of from inspiring English sources

Next we look, unlike Theorem 1.1, at [1, Theorem  2] in which Rockafellar achieved a linear convergence of the sequence by considering the Lipschitz continuity of at 0 instead.

Occasional qualifications in the light of later theory hint at a messier process than this, but the overall impression is of a linear convergence on the truth.

Note that if we set in Theorem 4.3, we get a result connecting [2] to the case of a linear convergence setting, but the algorithm remains overrelaxed (or superrelaxed).

There exist two types of MFD: one has at most a linear convergence rate and the other has a superlinear convergence rate.

From the general theory of Block-Relaxation algorithms (de Leeuw, 1994), it can be shown that Algorithm 1 has at least a linear convergence rate.

After presenting in Section 2 the needed preliminary material, we devote Section 3 to a proof of the global and linear convergence of the scheme (5a - 5d) under some assumptions.

A priori error estimates are proved from which, under suitable regularity conditions, the linear convergence of the algorithm is derived.

Moreover, linear convergence of the scheme is even characterized in terms of a novel quasi-orthogonality axiom (see Section  4.4).

The work  [49] introduced an appropriate quasi-orthogonality (B3a) in the H 1 -norm to prove linear convergence of the so-called total error which is the weighted sum of error plus oscillations.

A priori error estimates are proved from which, under adequate additional regularity conditions, the linear convergence of the algorithm is deduced.

Now we turn our attention (using the previous argument) to linear convergence of the sequence.