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 pro...
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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.
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 durin...
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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.
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 studie...
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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.
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 ...
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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
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 colle...
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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.
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 return...
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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.
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 alg...
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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.
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 return...
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ISBN:
(纸本)9781479903573
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.
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 ...
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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.
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...
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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.
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