The objective of the paper is to establish a computable upper bound for almost sure convergence rate class ratio consensus algorithms defined via column-stochastic matrices. Our result extends works Iutzeler et al. from 2013 on similar bounds that have been obtained in more restrictive setup with limited conclusions. present complements results by Gerencsér and 2022, identifying exact wi...

In this paper, we focus on a splitting method called the $ \theta $-scheme proposed by Glowinski and Le Tallec in [17,20,27]. First, present an elaborative convergence analysis Hilbert space propose general convergent inexact $-scheme. Second, for unconstrained problems, prove of show sublinear rate terms objective value. Furthermore, practical is derived to solve l_2 $-loss based problems its ...

Improved convergence rate estimates are derived for a variant of Aronszajn-type intermediate problems that is both computationally feasible and convergent for problems with nontrivial essential spectra. In a previous paper the authors obtained rate of convergence estimates for this method in terms of containment gaps between subspaces. In the present work, techniques for estimating relatively u...

3 Local convergence rate: simple case 2 3.1 Theorem statement . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 3 3.2 Main estimate . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 3 3.3 Convergence rate of the sequence . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 4 3.4 Proof of the theorem . . . . . . . . . . . . . . ....

We prove the trace-norm convergence of the Trotter product formula for nonself-adjoint Gibbs semigroups. For any m-sectorial generators A and B such that e ?tRe A is in the trace-class for t > 0, the Trotter product formula converges in the trace-norm. With smallness conditions on B with respect to A, we give error bound estimates of the convergence rate in this topology.