In this paper, three iterative forms of the LMS learning algorithm were tested for the calculation of the coefficients of FIR filters used as TV Ghost Cancellers. These computational forms are: the Stochastic Gradient...
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In this paper, three iterative forms of the LMS learning algorithm were tested for the calculation of the coefficients of FIR filters used as TV Ghost Cancellers. These computational forms are: the Stochastic Gradient Fixed-Step (SGLMS) [1] and a Variable Step (SLS-CD), [2] algorithms, as well as the Recursive Modified Gram-Schmidt RMGS algorithm [3]. Because of the iterative nature of the selected algorithms, they are very convenient to be used in on-line LTF filter coefficient adaptations. This makes it possible to compute the coefficient values of the ghost canceller, when the sampling of the signal generates a huge amount of data, which is very hard to be handled with a PC. The aforementioned algorithms are written in a very powerful and flexible matrix oriented software, and all the tests were performed using a very flexible TV System Simulator [4]. During the tests, fast convergence of the ghost canceller coefficients to the theoretical values [4] have been observed.
We present three different specifications of a read-write register that may occasionally return out-of-date values - namely, a (basic) random register, a P -random register, and a monotone random register. We show tha...
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We present three different specifications of a read-write register that may occasionally return out-of-date values - namely, a (basic) random register, a P -random register, and a monotone random register. We show that these specifications are implemented by the probabilistic quorum algorithm of Malkhi, Reiter, Wool, and Wright, and we illustrate how to program with such registers in the framework of Bertsekas, using the notation of Uresin and Dubois. Consequently, existing iterative algorithms for a significant class of problems (including solving systems of linear equations, finding shortest paths, constraint satisfaction, and transitive closure) will converge with high probability if executed in a system in which the shared data is implemented with registers satisfying the new specifications. Furthermore, the algorithms in this framework will inherit positive attributes concerning load and fault-tolerance from the underlying register implementation. The expected convergence time for iterative algorithms using the monotone implementation is analyzed and shown experimentally to improve on that of the original implementation. The message complexity for iterative algorithms using the monotone probabilistic quorum implementation is shown to improve on that of non-probabilistic implementations in a quantifiable situation.
In this paper, two iterative algorithms are proposed to solve stochastic algebraic Riccati matrix equations arising in the linear quadratic optimal control problem of linear stochastic systems with state-dependent noi...
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In this paper, two iterative algorithms are proposed to solve stochastic algebraic Riccati matrix equations arising in the linear quadratic optimal control problem of linear stochastic systems with state-dependent noise. In the first algorithm, a standard Riccati matrix equation needs to be solved at each iteration step, and in the second algorithm a standard Lyapunov matrix equation needs to be solved at each iteration step. In the proposed algorithms, a weighted average of the estimates in the last and the previous steps is used to update the estimate of the unknown variable at each iteration step. Some properties of the sequences generated by these algorithms under appropriate initial conditions are presented, and the convergence properties of the proposed algorithms are analyzed. Finally, two numerical examples are employed to show the effectiveness of the proposed algorithms. (C) 2018 Elsevier Inc. All rights reserved.
Two iterative minimax algorithms are presented with associated convergence theorems. Both algorithms consist of iterative procedures based on a sequence of finite parameter sets. In general, these finite parameter set...
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Two iterative minimax algorithms are presented with associated convergence theorems. Both algorithms consist of iterative procedures based on a sequence of finite parameter sets. In general, these finite parameter sets are subsets of an infinite parameter space. To show their applicabilities, several commonly used examples are presented. It is also shown that minimax problems with or without finite parameter sets can be solved by these two algorithms numerically to any assigned degree of accuracy.< >
Solving non-linear equation is perhaps one of the most difficult problems in all of numerical computations, especially in a diverse range of engineering applications. The convergence and performance characteristics ca...
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Solving non-linear equation is perhaps one of the most difficult problems in all of numerical computations, especially in a diverse range of engineering applications. The convergence and performance characteristics can be highly sensitive to the initial guess of the solution for most numerical methods such as Newton's method. However, it is very difficult to select reasonable initial guess of the solution for most systems of non-linear equations. Besides, the computational efficiency is not high enough. Taking this into account, based on variational iteration technique, we develop some new iterative algorithms for solving one-dimensional non-linear equations. The convergence criteria of these iterative algorithms has also been discussed. The superiority of the proposed iterative algorithms is illustrated by solving some test examples and comparing them with other well-known existing iterative algorithms in literature. In the end, the graphical comparison of the proposed iterative algorithms with other well-known iterative algorithms have been made by means of polynomiographs of different complex polynomials which reflect the fractal behavior and dynamical aspects of the proposed iterative algorithms.
This article focuses on the effect of both process topology and load balancing on various programming models for SMP clusters and iterative algorithms. More specifically, we consider nested loop algorithms with consta...
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This article focuses on the effect of both process topology and load balancing on various programming models for SMP clusters and iterative algorithms. More specifically, we consider nested loop algorithms with constant flow dependencies, that can be parallelized on SMP clusters with the aid of the tiling transformation. We investigate three parallel programming models, namely a popular message passing monolithic parallel implementation, as well as two hybrid ones, that employ both message passing and multi-threading. We conclude that the selection of an appropriate mapping topology for the mesh of processes has a significant effect on the overall performance, and provide an algorithm for the specification of such an efficient topology according to the iteration space and data dependencies of the algorithm. We also propose static load balancing techniques for the computation distribution between threads, that diminish the disadvantage of the master thread assuming all inter-process communication due to limitations often imposed by the message passing library. Both improvements are implemented as compile-time optimizations and are further experimentally evaluated. An overall comparison of the above parallel programming styles on SMP clusters based on micro-kernel experimental evaluation is further provided, as well.
The objective of this paper is to develop methods for solving image recovery problems subject to constraints on the solution. More precisely, we will be interested in problems which can be formulated as the minimizati...
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The objective of this paper is to develop methods for solving image recovery problems subject to constraints on the solution. More precisely, we will be interested in problems which can be formulated as the minimization over a closed convex constraint set of the sum of two convex functions f and g, where f may be nonsmooth and g is differentiable with a Lipschitz-continuous gradient. To reach this goal, we derive two types of algorithms that combine forward-backward and Douglas-Rachford iterations. The weak convergence of the proposed algorithms is proved. In the case when the Lipschitz-continuity property of the gradient of g is not satisfied, we also show that, under some assumptions, it remains possible to apply these methods to the considered optimization problem by making use of a quadratic extension technique. The effectiveness of the algorithms is demonstrated for two wavelet-based image restoration problems involving a signal-dependent Gaussian noise and a Poisson noise, respectively.
Some recent results are summarized concerning a class of algorithms known as regular iterative algorithms, particularly with respect to their implementations on processor arrays. Regular iterative algorithms contain a...
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Some recent results are summarized concerning a class of algorithms known as regular iterative algorithms, particularly with respect to their implementations on processor arrays. Regular iterative algorithms contain all algorithms executed by systolic arrays as a proper subclass and are therefore of considerable importance in real-time signal processing applications. Some general concepts concerning the design of parallel architectures are introduced, and the importance of devising special techniques that utilize any available structure in the algorithm is highlighted. A generic description of the existing methodologies for the systematic design of systolic arrays is given. Using some simple examples, the limitations of these methods are shown. A formal methodology is proposed that overcomes the difficulties in the existing procedures
MapReduce is the most popular framework for distributed processing. Recently, the scalability of data mining and machine learning algorithms has significantly improved with help from MapReduce. However, MapReduce does...
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MapReduce is the most popular framework for distributed processing. Recently, the scalability of data mining and machine learning algorithms has significantly improved with help from MapReduce. However, MapReduce does not handle iterative algorithms very efficiently. The problem is that many data mining and machine learning algorithms are iterative by nature. In order to overcome the limitations of MapReduce, many advanced distributed systems have been developed, including HaLoop, iMapReduce, Twister, and Spark. In this paper, we identify and categorize the limitations of MapReduce in handling iterative algorithms, and then, experimentally investigate the consequences of these limitations by using the most flexible and stable distributed system, Spark. According to our experiment results, the network I/O overhead was the primary factor that affected system performance the most. The disk I/O overhead also affected system performance, but it was less significant than the network I/O overhead. For the synchronization overhead, it affected system performance only when the static data was not cached.
We propose a method for accelerating iterative algorithms for solving symmetric linear complementarity problems. The method consists in performing a one-dimensional optimization in the direction generated by a splitti...
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We propose a method for accelerating iterative algorithms for solving symmetric linear complementarity problems. The method consists in performing a one-dimensional optimization in the direction generated by a splitting method even for non-descent directions. We give strong convergence proofs and present numerical experiments that justify using this acceleration.
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