convergence rate
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2022 ◽  
Vol 121 ◽  
pp. 105042
Yi Jiang ◽  
Weinan Gao ◽  
Jing Na ◽  
Di Zhang ◽  
Timo T. Hämäläinen ◽  

Agriculture ◽  
2022 ◽  
Vol 12 (1) ◽  
pp. 116
Binbin Mo ◽  
Mengyang Hou ◽  
Xuexi Huo

Climate change and farmland environmental pollution have put greater pressure on the sustainability of agricultural production. Based on the provincial panel data of mainland China from 1978 to 2018, climate variables such as precipitation, temperature, and sunshine hours are included into the input indicators, and agricultural non-point source pollution and carbon emissions are taken as undesirable outputs, the agricultural production efficiency (APE) under the dual constraints of climate change and the resource environment was estimated by the super slacks-based measure (SBM)-undesirable model. On the basis of the trajectory of the imbalanced spatiotemporal evolution of APE shown by Kernel density estimation and the standard deviational ellipse (SDE)–center of gravity (COG) transfer model, the spatial convergence model was used to test the convergence and differentiation characteristics of APE. Under the dual constraints, APE presents a “bimodal” distribution with a stable increase in fluctuation, but it is still at a generally low level and does not show polarization, among which the APE in the northeast region is the highest. The COG of APE tends to transfer towards the northeast, and the coverage of the SDE is shrinking, so the overall spatial pattern is characterized by a tendency of clustering towards the north in the north-south direction and a tendency of imbalance in the east-west direction. APE has significant spatial convergence, and there is a trend of “latecomer catching-up” in low-efficiency regions. The introduction of spatial correlation accelerates the convergence rate and shortens the convergence period. The convergence rate is the highest in the central and western regions, followed by that in the northeastern region, and the convergence rate is the lowest in the eastern region. In addition, the convergence rate in different time periods has a phase change. The process of improving the quality and efficiency of agricultural production requires enhancing the adaptability of climate change, balancing the carrying capacity of the resource environment, and strengthening inter-regional cooperation and linkage in the field of agriculture.

2022 ◽  
Hanne Kekkonen

Abstract We consider the statistical non-linear inverse problem of recovering the absorption term f>0 in the heat equation with given sufficiently smooth functions describing boundary and initial values respectively. The data consists of N discrete noisy point evaluations of the solution u_f. We study the statistical performance of Bayesian nonparametric procedures based on a large class of Gaussian process priors. We show that, as the number of measurements increases, the resulting posterior distributions concentrate around the true parameter generating the data, and derive a convergence rate for the reconstruction error of the associated posterior means. We also consider the optimality of the contraction rates and prove a lower bound for the minimax convergence rate for inferring f from the data, and show that optimal rates can be achieved with truncated Gaussian priors.

Pham Quy Muoi Pham

In [1], Nesterov has introduced an optimal algorithm with constant step-size,  with  is the Lipschitz constant of objective function. The algorithm is proved to converge with optimal rate . In this paper, we propose a new algorithm, which is allowed nonconstant step-sizes . We prove the convergence and convergence rate of the new algorithm. It is proved to have the convergence rate  as the original one. The advance of our algorithm is that it is allowed nonconstant step-sizes and give us more free choices of step-sizes, which convergence rate is still optimal. This is a generalization of Nesterov's algorithm. We have applied the new algorithm to solve the problem of finding an approximate solution to the integral equation.

Energies ◽  
2021 ◽  
Vol 15 (1) ◽  
pp. 197
Arobinda Dash ◽  
Durgesh Prasad Bagarty ◽  
Prakash Kumar Hota ◽  
Manoj Kumar Sahu ◽  
Twinkle Hazra ◽  

A control structure design of a three-phase three-leg four-wire grid-tied Distribution Static Synchronous Compensator (DSTATCOM) based on a combined-step-size real-coefficient improved proportionate affine projection sign algorithm (CSS-RIP-APSA) has been presented. The three-phase four-wire DSTATCOM is used for reactive power compensation along with harmonic current minimization. This strategy also helps in load balancing and neutral current compensation. The affine projection sign algorithm (APSA) is a member of the adaptive filter family, which has a slow convergence rate. The conventional adaptive filter deals with the trade-off between the convergence rate and the steady-state error. In the proposed algorithm, the RIP-APSA adaptive filter with two different step sizes has been designed to decrease the computational burden while achieving the advantages of a fast convergence rate and reduced steady-state error. The proposed controller also makes the inverter function a shunt compensator. The controller primarily evaluates the fundamental weight component of distorted load currents. The aim of the proposed system is to compensate for reactive power and to ensure unity power factor during the faulty conditions as well as for unbalancing grid conditions. The proposed control algorithm of the grid-tied DSTATCOM works effectively on the laboratory prototype as verified from the experimental results.

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