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排序方式: 共有2513条查询结果,搜索用时 15 毫秒
1.
In this paper, we study the local linear convergence properties of a versatile class of Primal–Dual splitting methods for minimizing composite non-smooth convex optimization problems. Under the assumption that the non-smooth components of the problem are partly smooth relative to smooth manifolds, we present a unified local convergence analysis framework for these methods. More precisely, in our framework, we first show that (i) the sequences generated by Primal–Dual splitting methods identify a pair of primal and dual smooth manifolds in a finite number of iterations, and then (ii) enter a local linear convergence regime, which is characterized based on the structure of the underlying active smooth manifolds. We also show how our results for Primal–Dual splitting can be specialized to cover existing ones on Forward–Backward splitting and Douglas–Rachford splitting/ADMM (alternating direction methods of multipliers). Moreover, based on these obtained local convergence analysis result, several practical acceleration techniques are discussed. To exemplify the usefulness of the obtained result, we consider several concrete numerical experiments arising from fields including signal/image processing, inverse problems and machine learning. The demonstration not only verifies the local linear convergence behaviour of Primal–Dual splitting methods, but also the insights on how to accelerate them in practice. 相似文献
2.
Erosion and sediments transport processes have a great impact on industrial structures and on water quality. Despite its limitations, the Saint‐Venant‐Exner system is still (and for sure for some years) widely used in industrial codes to model the bedload sediment transport. In practice, its numerical resolution is mostly handled by a splitting technique that allows a weak coupling between hydraulic and morphodynamic distinct softwares but may suffer from important stability issues. In recent works, many authors proposed alternative methods based on a strong coupling that cure this problem but are not so trivial to implement in an industrial context. In this work, we then pursue 2 objectives. First, we propose a very simple scheme based on an approximate Riemann solver, respecting the strong coupling framework, and we demonstrate its stability and accuracy through a number of numerical test cases. However, second, we reinterpret our scheme as a splitting technique and we extend the purpose to propose what should be the minimal coupling that ensures the stability of the global numerical process in industrial codes, at least, when dealing with collocated finite volume method. The resulting splitting method is, up to our knowledge, the only one for which stability properties are fully demonstrated. 相似文献
3.
Yaping Chen Dr. Kun Rui Prof. Jixin Zhu Prof. Shi Xue Dou Dr. Wenping Sun 《Chemistry (Weinheim an der Bergstrasse, Germany)》2019,25(3):703-713
Developing clean and sustainable energies as alternatives to fossil fuels is in strong demand within modern society. The oxygen evolution reaction (OER) is the efficiency-limiting process in plenty of key renewable energy systems, such as electrochemical water splitting and rechargeable metal–air batteries. In this regard, ongoing efforts have been devoted to seeking high-performance electrocatalysts for enhanced energy conversion efficiency. Apart from traditional precious-metal-based catalysts, nickel-based compounds are the most promising earth-abundant OER catalysts, attracting ever-increasing interest due to high activity and stability. In this review, the recent progress on nickel-based oxide and (oxy)hydroxide composites for water oxidation catalysis in terms of materials design/synthesis and electrochemical performance is summarized. Some underlying mechanisms to profoundly understand the catalytic active sites are also highlighted. In addition, the future research trends and perspectives on the development of Ni-based OER electrocatalysts are discussed. 相似文献
4.
P. Seelig A. Dax S. Faber M. Gerlach G. Huber T. Kühl D. Marx P. Merz W. Quint F. Schmitt H. Winter M. Würtz 《Hyperfine Interactions》1998,114(1-4):135-139
The investigation of the 1s HFS provides a good possibility for testing QED effects in a combination of a strong electric
and magnetic field. Here, we report about the laserspectroscopic measurements of the ground state hyperfine splitting in 207Pb81+. To handle this M1-transition in the infrared optical regime with its long lifetime, we developed a new detection technique
using a bunched ion beam. For the observation of fluorescence light, a new mirror system is adapted to the emission characteristics
from an ion beam at relativistic velocities.
This revised version was published online in July 2006 with corrections to the Cover Date. 相似文献
5.
Kasper K. Berthelsen Jesper Møller 《Bulletin of the Brazilian Mathematical Society》2002,33(3):351-367
This primer provides a self-contained exposition of the case where spatial birth-and-death processes are used for perfect
simulation of locally stable point processes. Particularly, a simple dominating coupling from the past (CFTP) algorithm and
the CFTP algorithms introduced in [13], [14], and [5] are studied. Some empirical results for the algorithms are discussed.
Received: 30 June 2002 相似文献
6.
7.
By further generalizing the skew-symmetric triangular splitting iteration method studied by Krukier, Chikina and Belokon (Applied Numerical Mathematics, 41 (2002), pp. 89–105), in this paper, we present a new iteration scheme, called the modified skew-Hermitian triangular splitting iteration method, for solving the strongly non-Hermitian systems of linear equations with positive definite coefficient matrices. We discuss the convergence property and the optimal parameters of this new method in depth. Moreover, when it is applied to precondition the Krylov subspace methods like GMRES, the preconditioning property of the modified skew-Hermitian triangular splitting iteration is analyzed in detail. Numerical results show that, as both solver and preconditioner, the modified skew-Hermitian triangular splitting iteration method is very effective for solving large sparse positive definite systems of linear equations of strong skew-Hermitian parts. 相似文献
8.
We consider a splitting finite-difference scheme for an initial-boundary value problem for a two-dimensional nonlinear evolutionary
equation. The problem is split into nonlinear and linear parts. The linear part is also split into locally one-dimensional
equations. We prove the convergence and stability of the scheme in L
2 and C norms.
Printed in Lietuvos Matematikos Rinkinys, Vol. 45, No. 3, pp. 413–434, July–September, 2005. 相似文献
9.
Identification of nonlinear elliptic equations 总被引:1,自引:0,他引:1
An optimization theoretic approach and algorithm for the estimation of state-dependent coefficients in nonlinear elliptic equation is presented. It is based on a splitting method combined with convex analysis techniques. Convergence of the algorithm is established and numerical examples are included.The research of K. Kunisch was supported in part by a grant from the Bundesministerium für Wissenschaft und Forschung, Austria. 相似文献
10.
Richard Becker Mladen Prester Ping Hui Lin Mats Johnsson Ivica Zivkovic 《Journal of solid state chemistry》2007,180(3):1051-1059
Two new isostructural cobalt selenite halides Co5(SeO3)4Cl2 and Co5(SeO3)4Br2 have been synthesized. They crystallize in the triclinic system space group P−1 with the following lattice parameters for Co5(SeO3)4Cl2: a=6.4935(8) Å, b=7.7288(8) Å, c=7.7443(10) Å, α=66.051(11)°, β=73.610(11)°, γ=81.268(9)°, and Z=1. The crystal structures were solved from single-crystal X-ray data, R1=3.73 and 4.03 for Co5(SeO3)4Cl2 and Co5(SeO3)4Br2, respectively. The new compounds are isostructural to Ni5(SeO3)4Br2.Magnetic susceptibility measurements on oriented single-crystalline samples show anisotropic response in a broad temperature range. The anisotropic susceptibility is quantitatively interpreted within the zero-field splitting schemes for Co2+ and Ni2+ ions. Sharp low-temperature susceptibility features, at TN=18 and 20 K for Co5(SeO3)4Cl2 and Co5(SeO3)4Br2, respectively, are ascribed to antiferromagnetic ordering in a minority magnetic subsystem. In isostructural Ni5(SeO3)4Br2 magnetically ordered subsystem represents a majority fraction (TN=46 K). Nevertheless, anisotropic susceptibility of Ni5(SeO3)4Br2 is dominated at low temperatures by a minority fraction, subject to single-ion anisotropy effects and increasing population of Sz=0 (singlet) ground state of octahedrally coordinated Ni2+. 相似文献