We extend a result of Nashed and Engl (1979) on fixed points of nonlinear random operators by using iterative methods to the case of nonlinear random operators on product spaces. The obtained result in a way is a prob...
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We extend a result of Nashed and Engl (1979) on fixed points of nonlinear random operators by using iterative methods to the case of nonlinear random operators on product spaces. The obtained result in a way is a probabilistic (stochastic) version of the deterministic fixed point theorems in product spaces by Kirk (1989), Kirk and Sternfeld (1984), Kirk and Yanez (1988), Tan and Xu(1991), and others. (C) 1995 Academic Press, Inc.
Here we consider the solvability based on iterative algorithms of the generalized variational inequalities and associated nonlinear equations involving multivalued relaxed Lipschitz operators.
Here we consider the solvability based on iterative algorithms of the generalized variational inequalities and associated nonlinear equations involving multivalued relaxed Lipschitz operators.
Let H-1, H-2 be real Hilbert spaces, C subset of H-1 be a nonempty closed convex set, and 0 is not an element of C. Let A : H-1 -> H-2, B : H-1 -> H-2 be two bounded linear operators. We consider the problem to ...
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Let H-1, H-2 be real Hilbert spaces, C subset of H-1 be a nonempty closed convex set, and 0 is not an element of C. Let A : H-1 -> H-2, B : H-1 -> H-2 be two bounded linear operators. We consider the problem to find x is an element of C such that Ax = -Bx (0 = Ax + Bx). Recently, Eckstein and Svaiter presented some splitting methods for finding a zero of the sum of monotone operator A and B. However, the algorithms are largely dependent on the maximal monotonicity of A and B. In this paper, we describe some algorithms for finding a zero of the sum of A and B which ignore the conditions of the maximal monotonicity of A and B.
iterative algorithms such as Newton's method for square-root extraction offer attractive low-cost techniques for function computation but invariably operate at low-speed. Such algorithms are even more feasible whe...
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iterative algorithms such as Newton's method for square-root extraction offer attractive low-cost techniques for function computation but invariably operate at low-speed. Such algorithms are even more feasible when one considers their use in conjunction with currently available microprocessors. In this letter, two particular iterative algorithms are described and evaluated. These are for the computation of arc (cos (p))/() and cos (p). Error results are given which show that the accuracy for many instrumentation-type applications is tolerable when a small number of iterations, say, 16, is involved.
In this paper, the m-machine no-wait flowshop scheduling problem with sequence-dependent setup times is considered to minimize the makespan. According to the problem characteristics, the increment properties of some f...
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ISBN:
(纸本)9781467355322;9781467355339
In this paper, the m-machine no-wait flowshop scheduling problem with sequence-dependent setup times is considered to minimize the makespan. According to the problem characteristics, the increment properties of some fundamental operators of algorithms are analyzed. Two increment-based methods FSP (fittest swap points) and FMP (fittest move points) are constructed for fast evaluation on all algorithms. Four iterative algorithms on the basis of job insert, move and swap operators are proposed for the considered problem. In IMS (heuristic with insert, move and swap operators) algorithm, the current solution is constructed step by step by inserting a job at a time and is improved by conducting jobs move within a certain range. FR-IMS (full-range IMS) algorithm is a full-range IMS algorithm. Both IA (iterative algorithm) and IALS (iterative algorithm with local search) algorithms consist of two phases: solution initialization according to a certain rule and solution enhancement by iteratively conducting perturbation and move-based techniques. The main difference between IA and IALS lies in the fact that, instead of using FMP method in the enhancement phase like IA, a local search process which is based on moves under a first-improvement type of pivoting rule as well as a restart mechanism is adopted in IALS. Experimental results show that the proposed algorithms outperform the best existing approaches, among which IALS is the most effective one.
This research investigates the problem of robust static resource allocation for a large class of clusters processing periodically updated data sets under an imposed quality of service constraint. The target hardware p...
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ISBN:
(纸本)9780889866386
This research investigates the problem of robust static resource allocation for a large class of clusters processing periodically updated data sets under an imposed quality of service constraint. The target hardware platform consists of a number of sensors generating input for heterogeneous applications continuously executing on a set of heterogeneous compute nodes. In practice such systems are expected to function in a physical environment replete with uncertainty, which causes the amount of processing required over time to fluctuate substantially. Determining a resource allocation that accounts for this uncertainty in a way that can provide a probabilistic guarantee that a given level of QoS is achieved is an important research problem. The stochastic robustness metric is based on a mathematical model where the relationship between uncertainty in system parameters and its impact on system performance is described stochastically. The established metric is then used in the design of several resource allocation algorithms utilizing evolutionary approaches. The performance results and comparison analysis are presented for a simulated environment that replicates a heterogeneous cluster-based processing center for a radar system.
The purpose of this paper is to prove the iterative processes generated by a nonexpansive semigroup and a generalized contraction mapping converge strongly to common fixed point p of the nonexpansive semigroup, and p ...
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ISBN:
(纸本)9783642181337
The purpose of this paper is to prove the iterative processes generated by a nonexpansive semigroup and a generalized contraction mapping converge strongly to common fixed point p of the nonexpansive semigroup, and p is the unique solution to some variational inequality. The result extends some theorems in the literature.
To investigate the stabilization problem of the periodic linear systems, it is important to achieve the solution of the periodic Lyapunov matrix equation. In order to find the solution of the equation, novel iterative...
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ISBN:
(纸本)9789881563958
To investigate the stabilization problem of the periodic linear systems, it is important to achieve the solution of the periodic Lyapunov matrix equation. In order to find the solution of the equation, novel iterative algorithms for discrete-time periodic Lyapunov equations are derived, respectively to the zero initial conditions and arbitrary initial conditions. What's more, the latest information estimation theory is utilized in the iterative algorithm. The validity of the algorithms are verified by numerical simulations.
This paper addresses the use of multiplicative iterative algorithms to compute the abundances in unmixing of hyperspectral pixels. The advantage of iterative over direct methods is that they allow incorporation of pos...
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ISBN:
(纸本)0819449539
This paper addresses the use of multiplicative iterative algorithms to compute the abundances in unmixing of hyperspectral pixels. The advantage of iterative over direct methods is that they allow incorporation of positivity and sum-to-one constraints of the abundances in an easy fashion while also allowing better regularization of the solution for the ill-conditioned case. The derivation of two iterative algorithms based on minimization of least squares and Kulback-Leibler distances are presented. ne resulting algorithms are the same as the ISRA and EMML algorithms presented in the emission tomography literature respectively. We show that the ISRA algorithm and not the EMML algorithm computes the maximum likelihood estimate of the abundances under Gaussian assumptions while the EMML algorithm computes a minimum distance solution based on the Kulback-Leibler generalized distance. In emission tomography, the EMML computes the maximum likelihood estimate of the reconstructed image. We also show that, since the unmixing problem is in general overconstrained and has no solutions, acceleration techniques for the EMML algorithm such as the RBI-EMML will not converge.
The problem treated in this work is the numerical solution of the complete eigenspectrum for Hermitian Toeplitz matrices. The core procedure utilized is Trench's algorithm which employs bisection on contiguous int...
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The problem treated in this work is the numerical solution of the complete eigenspectrum for Hermitian Toeplitz matrices. The core procedure utilized is Trench's algorithm which employs bisection on contiguous intervals and the Pegasus method to achieve estimates of distinct eigenvalues. Several modifications to Trench's algorithm are examined, the goals being an increase in the rate of convergence, even at some reduction in estimate accuracy, and an accommodation of eigenvalue multiplicity, or, practically speaking, eigenvalue clustering. A promising approach is found which contains three key ingredients: 1) a modification of Trench's procedure to employ noncontiguous intervals, 2) an addition of a procedure for multiplicity identification, and 3) a replacement of the Pegasus method by the modified Rayleigh quotient iteration (MRQI) of Hu and Kung. The result is the basis for a novel eigenspectrum solver possessing cubic convergence rate and good estimation accuracy. Simulation results are provided for high order Hermitian Toeplitz matrices.
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