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splitting algorithms FOR NUMERICAL SOLUTION OF NAVIER - STOKES EQUATIONS IN FLUID DYNAMICS PROBLEMS

JOURNAL OF APPLIED MECHANICS AND TECHNICAL PHYSICS 2021年第3期62卷 391-400页

作者： Kovenya, V. M. Fed Res Ctr Informat & Computat Technol Novosibirsk 630090 Russia Novosibirsk State Univ Novosibirsk 630090 Russia

Implicit finite-volume predictor-corrector algorithms based on the splitting method are proposed for the numerical solution of the Navier - Stokes equations written in integral form for a compressible gas, and the properties of these algorithms are investigated. An economical algorithm for splitting equations into physical processes and spatial variables is considered. Numerical solutions of two-dimensional and spatial fluid dynamics problems are determined and compared with the known computational results. It can be concluded on the basis of the estimates obtained and calculations performed that the proposed algorithms are effective.

关键词： Navier Stokes equations finite-volume schemes splitting algorithms supersonic flows

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splitting algorithms FOR RARE EVENT SIMULATION OVER LONG TIME INTERVALS

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ANNALS OF APPLIED PROBABILITY 2020年第6期30卷 2963-2998页

作者： Buijsrogge, Anne Dupuis, Paul Snarski, Michael Univ Twente Fac Elect Engn Math & Comp Sci Enschede Netherlands Brown Univ Div Appl Math Providence RI 02912 USA

In this paper we study the performance of splitting algorithms, and in particular the RESTART method, for the numerical approximation of the probability that a process leaves a neighborhood of a metastable point during some long time interval [0, T]. We show that, in contrast to alternatives such as importance sampling, the decay rate of the second moment does not degrade as T -> infinity. In the course of the analysis we develop some related large deviation estimates that apply when the time interval of interest depends on the large deviation parameter.

关键词： splitting algorithms RESTART Monte Carlo methods large deviations metastable points

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Linear Convergence Rate of splitting algorithms for Multi-Block Constrained Convex Minimizations

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IEEE ACCESS 2020年 8卷 120694-120700页

作者： Deng, Xiaoge Liu, Feng Huang, Feng Natl Univ Def Technol Coll Comp Natl Lab Parallel & Distributed Proc PDL Changsha 410073 Peoples R China

Multi-block linear constrained separable convex minimizations are ubiquitous and have been drawing increasing attention in recent researches. The alternating direction method of multipliers (ADMM) has been well studied and used in the literature for the two-block case. However, the direct extension of the ADMM to the multi-block case is not necessarily convergent. ADMM with Gaussian Back Substitution and ADMM with Prox-Parallel splitting are two useful schemes to deal with the multi-block situation. Nevertheless, only a sublinear convergence rate was given in previous studies. In this paper, we prove the linear convergence rate of these two schemes under some assumptions. The proofs mainly depend on the variational inequalities.

关键词： Multi-block alternating direction method of multipliers linear convergence rate variational inequalities splitting algorithms

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New splitting algorithms for geometric transformations of digital images and their error analysis

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INTERNATIONAL JOURNAL OF IMAGING SYSTEMS AND TECHNOLOGY 2011年第4期21卷 323-335页

作者： Li, Zi-Cai Chiang, John Y. Suen, C. Y. Natl Sun Yat Sen Univ Dept Comp Sci & Engn Kaohsiung 80424 Taiwan Natl Sun Yat Sen Univ Dept Appl Math Kaohsiung 80424 Taiwan Concordia Univ Ctr Pattern Recognit & Machine Intelligence Montreal PQ H3G 1M8 Canada

For digital images and patterns under the nonlinear geometric transformation, T: (xi, eta) > (x, y), this study develops the splitting algorithms (i.e., the pixel-division algorithms) that divide a 2D pixel into N x N subpixels, where N is a positive integer chosen as N = 2(k)(k >= 0) in practical computations. When the true intensity values of pixels are known, this method makes it easy to compute the true intensity errors. As true intensity values are often unknown, the proposed approaches can compute the sequential intensity errors based on the differences between the two approximate intensity values at N and N/2. This article proposes the new splittingshooting method, new splitting integrating method, and their combination. These methods approximate results show that the true errors of pixel intensity are O(H), where H is the pixel size. Note that the algorithms in this article do not produce any sequential errors as N >= N(0), where N(0) (>= 2) is an integer independent of N and H. This is a distinctive feature compared to our previous papers on this subject. The other distinct feature of this article is that the true error bound O(H) is well suited to images with all kinds of discontinuous intensity, including scattered pixels. (C) 2011 Wiley Periodicals, Inc. Int J Imaging Syst Technol, 21, 323335, 2011

关键词： image geometric transformation digital images splitting algorithms splitting-shooting method error analysis

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Reliability-Based splitting algorithms for Time-Constrained Distributed Detection in Random-Access WSNs

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IEEE TRANSACTIONS ON SIGNAL PROCESSING 2014年第21期62卷 5536-5551页

作者： Laitrakun, Seksan Coyle, Edward J. Georgia Inst Technol Atlanta GA 30309 USA Georgia Inst Technol Sch Elect & Comp Engn Atlanta GA 30332 USA

We consider distributed detection applications for a wireless sensor network (WSN) that has a limited time to collect and process local decisions to produce a global decision. When this time is not sufficient to collect decisions from all nodes in the network, a strategy is needed for collecting those with the highest reliability. This can be accomplished by incorporating a reliability-based splitting algorithm into the random access protocol of the WSN: the collection time is divided into frames and only nodes with a specified range of reliabilities compete for the channel using slotted ALOHA within each frame-nodes with the most reliable decisions attempt transmission in the first frame, nodes with the next most reliable set of decisions attempt in the next frame, etc. The detection error probability (DEP) of the proposed scheme is minimized, and the efficacy is maximized by determining the reliability intervals that define which nodes attempt to transmit in each frame. Intervals that maximize the channel throughput do not always minimize the DEP or maximize the efficacy. Because the scheme orders transmissions of the local decisions in approximately descending order of reliability but suffers collisions, it will offer better performance than a collision-free scheme with no reliability ordering when the time constraint prevents transmission of all local decisions. The transition point between the two schemes is found by deriving the asymptotic relative efficiency (ARE) of the proposed scheme relative to a TDMA-based scheme.

关键词： Binary sensor networks censoring sensors distributed detection ordered transmissions random-access protocols splitting algorithms wireless sensor networks

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ONLINE ROBUST PORTFOLIO RISK MANAGEMENT USING TOTAL LEAST-SQUARES AND PARALLEL splitting algorithms

ONLINE ROBUST PORTFOLIO RISK MANAGEMENT USING TOTAL LEAST-SQ...

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IEEE International Conference on Acoustics, Speech, and Signal Processing (ICASSP)

作者： Slavakis, Konstantinos Leus, Geert Giannakis, Georgios B. Univ Minnesota Digital Technol Ctr Minneapolis MN 55455 USA Delft Univ Technol Dept Microelect Delft Netherlands

ISBN: (纸本)9781479903566

The present paper introduces a novel online asset allocation strategy which accounts for the sensitivity of Markowitz-inspired portfolios to low-quality estimates of the mean and the correlation matrix of stock returns. The proposed methodology builds upon the total least-squares (TLS) criterion regularized with sparsity attributes, and the ability to incorporate additional convex constraints on the portfolio vector. To solve such an optimization task, the present paper draws from the rich family of splitting algorithms to construct a novel online splitting algorithm with computational complexity that scales linearly with the number of unknowns. Real-world financial data are utilized to demonstrate the potential of the proposed technique.

关键词： Markowitz portfolio total least-squares sparsity splitting algorithms proximal mapping projection

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High accuracy splitting algorithms for the time-dependent Schrodinger equation with a train of laser pulses

High accuracy splitting algorithms for the time-dependent Sc...

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2003 Saratov Fall Meeting

作者： Gusev, AA Chuluunbaatar, O Vinitsky, SI Kaschiev, MS Joint Nucl Res Inst Dubna Russia

ISBN: (纸本)0819453994

High accuracy splitting algorithms based on the unitary approximations of the evolution operator for the time-dependent Schrodinger equation (TDSE) with a train of laser pulses are developed. The efficiency of the algorithms is shown using typical examples of a hydrogen atom affected by a train of laser pulses in the dipole approximation and an additional constant magnetic field. The stabilization effects are discussed.

关键词： splitting algorithms Schrodinger equation unitary approximations evolution operator atoms interacting with laser pulses

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ONLINE ROBUST PORTFOLIO RISK MANAGEMENT USING TOTAL LEAST-SQUARES AND PARALLEL splitting algorithms

ONLINE ROBUST PORTFOLIO RISK MANAGEMENT USING TOTAL LEAST-SQ...

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IEEE International Conference on Acoustics, Speech, and Signal Processing

作者： Konstantinos Slavakis Geert Leus Georgios B. Giannakis University of Minnesota Digital Technology Center Minneapolis USA Delft University of Technology Dept. of Microelectronics Delft The Netherlands

ISBN: (纸本)9781479903573

关键词： Markowitz portfolio total least-squares sparsity splitting algorithms proximal mapping projection

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An inertial projective splitting method for the sum of two maximal monotone operators

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COMPUTATIONAL & APPLIED MATHEMATICS 2025年第1期44卷 1-34页

作者： Penton Machado, Majela Univ Fed Bahia Inst Matemat & Estat Campus Ondina Ave Adhemar Barros S-N BR-40170110 Salvador BA Brazil

We propose a projective splitting type method to solve the problem of finding a zero of the sum of two maximal monotone operators. Our method considers inertial and relaxation steps, and also allows inexact solutions of the proximal subproblems within a relative-error criterion. We study the asymptotic convergence of the method, as well as its iteration-complexity. We also discuss how the inexact computations of the proximal subproblems can be carried out when the operators are Lipschitz continuous. In addition, we provide numerical experiments comparing the computational performance of our method with previous (inertial and non-inertial) projective splitting methods.

关键词： splitting algorithms Inertial algorithms Relative error Maximal monotone operators Complexity

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A Variational Approach to the Design of Multivariable Discrete-Time Supertwisting-Like algorithms

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IEEE TRANSACTIONS ON AUTOMATIC CONTROL 2025年第4期70卷 2495-2506页

作者： Miranda-Villatoro, Felix A. Univ Grenoble Alpes CNRS Grenoble INP Lab Jean KuntzmannCtr Inria F-38000 Grenoble France

In this article, a family of discrete-time, supertwisting-like algorithms is presented. The algorithms are naturally vector-valued and are described in an implicit fashion, reminiscent of backward-Euler discretization schemes. The well-posedness of the closed-loop is established and the robust stability, against a family of external disturbances, is thoroughly studied. Implementation strategies, involving splitting-algorithms from convex optimization, are also discussed and compared. Finally, numerical simulations show the performance of the proposed schemes.

关键词： Stability analysis Emulation Robustness Digital computers Thermal stability Numerical stability Context modeling Asymptotic stability Wind energy conversion Trajectory tracking Convex optimization discrete-time systems proximal-point algorithms robustness sliding-mode control splitting algorithms

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