In this lecture, we discuss splitting algorithms for convex minimization problems with objective given by the sum of two nonsmooth functions. We start with the fixed point property of such problems and derive a general scheme of splitting algorithm based on fixed point iteration. This covers Douglas-Rachford splitting and Peaceman-Rachford splitting algorithms. We also discuss the convergence r...

this study was done to evaluate the effects of harvest time on some factor of ‘ahmadaqaie’ pistachio nuts in rafsanjan. in three consecutive years (2009-2012) during three stages of friut ripening (40, 70 and 100 percent of hulling), fruit was harvested and physiological and biochemical parameters were measured. the experiments were conducted as randomized complete block design with compound an...

It is shown that the encoding/decoding problem for any asynchronous M -user memoryless multiple-access channel can be reduced to corresponding problems for at most 2M 1 single-user memoryless channels. This is done via a method called time-splitting multiple-access which is closely related to a recently developed method called rate-splitting multiple access. It is also related to to multilevel ...

Abstract. The Modified Phase Field Crystal (MPFC) equation, a generalized damped wave equation for which the usual Phase Field Crystal (PFC) equation is a special case, is analyzed in detail in three dimensions. A time-discrete numerical scheme, based on a convex splitting for the functional energy, is utilized to construct an approximate solution, which is then shown to converge to a solution ...

We consider the problem of splitting an order for R goods, R ≥ 1, among a set of sellers, each having bounded amounts of the goods, so as to minimize the total cost of the deal. In deal splitting with packages (DSP), the sellers offer packages containing combinations of the goods; in deal splitting with price tables (DST), the buyer can generate such combinations using price tables. Our problem...

In this paper, we present and analyze an energy-conserving linearly implicit scheme for solving the nonlinear wave equations. Optimal error estimates in time superconvergent space are established without certain time-step restrictions. The key is to estimate directly solution bounds H2-norm both equation corresponding fully discrete scheme, while previous investigations rely on temporal-spatial...

In this paper, we present an approach to deal with the dynamics of Dirac equation time-dependent electromagnetic potentials using fourth-order compact time-splitting method ($S_\text{4c}$). To purpose, time-ordering technique for Hamiltonians is introduced, so that influence time-dependence could be limited certain steps which are easy treat. Actually, in case equation, it turns out only those ...