The double backward splitting method, with iteration given by y k = ( I + λ k B ) − 1 x k, x k + 1 = ( I + λ k A ) − 1 y k, where { λ k } ⊆ ( 0, ∞ ) a sequence of regularization parameters.
Convergence results for the scheme (i), in the case in which { ρ k } is contained in a compact subset of ( 0, 1 ), can be found in [2]; the convergence analysis of the double backward scheme given by (ii), which can be found in [3] and [4]; the standard convergence analysis for (iii) one can see [5].
For instance, the double-backward method ofPassty [4] generates a sequence in the recursive manner: (1.1).
It is well known [5] that the sequence generated by the double-backward method (1.1) failsto converge weakly, in general.
All splitting methods can be essentially divided into three classes: Douglas/Peaceman-Rachford class (see, e.g., [17, 18]), the double-backward class (see, e.g., [19]), and the forward-backward class (see, e.g., [20, 21]).
If, moreover, α n ≡ 0, β n ≡ 0, then (2.7) becomes the so-called double-backward iterative scheme for the m-d-accretive mapping A: { x 1 ∈ E, y n = ( I + r n A ) − 1 x n, x n + 1 = ( I + s n A ) − 1 y n, n ≥ 1. (2.8).
The performance evaluation of these lubricants was conducted using the double cup backward extrusion test developed at the Engineering Research Center for Net Shape Manufacturing ERC/NSMM).
Kowroski doubled over backward; she danced upside down; she spiralled down la Cour's leg like a snake on a stick.
And it says a lot about this latest collaboration between Mr. Reed and Mr. Wilson that "Perfect Day," with its double-edged backward glance, turns out to be infinitely more haunting than this "Raven," which lies on the stage here like a dead and distinctly nonthreatening bird.
Weaknesses in the pawn structure, such as isolated, doubled, or backward pawns and holes, once created, are often permanent.
Pawn structure: Players strive to avoid the creation of pawn weaknesses such as isolated, doubled, or backward pawns, and pawn islands – and to force such weaknesses in the opponent's position.
