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AN ALGORITHM FOR A GENERALIZATION OF THE RICHARDSON EXTRAPOLATION PROCESS

SIAM JOURNAL ON NUMERICAL ANALYSIS 1987年第5期24卷 1212-1232页

作者： FORD, WF SIDI, A TECHNION ISRAEL INST TECHNOL DEPT COMP SCIIL-32000 HAIFAISRAEL

In this paper we present a recursive method, designated the $W^{(m)} $ algorithm, for implementing a generalization of the Richardson extrapolation process that has been ntroduced in [8]. Compared to the direct solution of the linear systems of equations defining the extrapolation procedure, this method requires a small number of arithmetic operations and very little storage. The technique is also applied to solve recursively the coefficient problem associated with the rational approximations obtained by applying the d-transformation of [6], [13] to power series. In the course of development a new recursive algorithm for implementing a very general extrapolation procedure is introduced, which is similar to that given in [2], [4] for solving the same problem. A FORTRAN program for the $W^{(m)} $algorithm is also appended.

关键词： 65B05 40A25 convergence acceleration generalized Richardson extrapolation recursive algorithms

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Constructing Stable recursive Schemes of Solving Overdetermined Systems of Linear Equations

Constructing Stable Recursive Schemes of Solving Overdetermi...

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8th IFAC Conference on Manufacturing Modelling, Management and Control (MIM)

作者： Chernyshov, K. R. Jharko, E. Ph. VA Trapeznikov Inst Control Sci 65 Profsoyuznaya Moscow 117997 Russia

The paper deals with a problem of solving overdetermined systems of linear algebraic equations. From a numerical method point of view, such a problem relates, in entity, to the Least Squares class. A feature of the present paper problem statement is that the system coefficients are not known and are replaced with corresponding random values that are sequentially observed. Solving the problem is focused on deriving an iterative/recursive algorithm that would be able to form a strongly consistent, i.e. converging with probability 1, sequence of estimates of the desired solution, and being stable with regard to the observation data and to the condition number of current estimates of the system matrix. (C) 2016, IFAC (International Federation of Automatic Control) Hosting by Elsevier Ltd. All rights reserved.

关键词： Condition number Instrumental variables Least squares Linear Equations Systems Parameter estimation recursive algorithms

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A Stochastic Majorize-Minimize Subspace Algorithm for Online Penalized Least Squares Estimation

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IEEE TRANSACTIONS ON SIGNAL PROCESSING 2017年第18期65卷 4770-4783页

作者： Chouzenoux, Emilie Pesquet, Jean-Christophe INRIA Saclay Ctr Visual Comp F-92295 Chatenay Malabry France Univ Paris Est CNRS LIGM UMR 8049 F-77454 Marne La Vallee France Univ Paris Saclay Cent Supelec Ctr Visual Comp F-92295 Chatenay Malabry France

Stochastic approximation techniques play an important role in solving many problems encountered in machine learning or adaptive signal processing. In these contexts, the statistics of the data are often unknown a priori or their direct computation is too intensive, and they have thus to be estimated online from the observed signals. For batch optimization of an objective function being the sum of a data fidelity term and a penalization (e.g., a sparsity promoting function), Majorize-Minimize (MM) methods have recently attracted much interest since they are fast, highly flexible, and effective in ensuring convergence. The goal of this paper is to show how these methods can be successfully extended to the case when the data fidelity term corresponds to a least squares criterion and the cost function is replaced by a sequence of stochastic approximations of it. In this context, we propose an online version of an MM subspace algorithm and we study its convergence by using suitable probabilistic tools. Simulation results illustrate the good practical performance of the proposed algorithm associated with a memory gradient subspace, when applied to both nonadaptive and adaptive filter identification problems.

关键词： Stochastic approximation optimization subspace algorithms memory gradient methods descent methods recursive algorithms majorization-minimization filter identification Newton method sparsity machine learning adaptive filtering

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Wang-Ball Triangular Patch and Its Properties

Wang-Ball Triangular Patch and Its Properties

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6th International Conference on Computer Graphics, Imaging and Visualization (CGIV 2009)

作者： Sukjaitham, Supareuk Dejdumrong, Natasha King Mongkuts Univ Technol Thonburi Dept Comp Engn Bangkok 10140 Thailand

ISBN: (纸本)9780769537894

A new model of triangular Ball surface is proposed with its quadratic complexity. It can be constructed from the idea of Wang-Ball univaritate functions and Wang algorithm. The new bivariate basis functions look analogous to the Wang-Ball polynomials. Evaluating points on a curve can be calculated from the new recursive algorithm that is proved to be quadratic, O(n(2)). Thus, the calculation time is less than any other triangular curves. Finally several important geometric properties for these surfaces are also identified such as normality, convexity and symmetry.

关键词： Triangular Ball Surfaces recursive algorithms

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On formal descriptions for knitting recursive patterns

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JOURNAL OF MATHEMATICS AND THE ARTS 2008年第1期2卷 9-27页

作者： Bernasconi, Anna Bodei, Chiara Pagli, Linda Univ Pisa Dipartimento Informat Pisa Italy

We investigate relationships between knitting and formal systems. We show how formal languages, grammars, and algorithms give rise to powerful tools that can be used in both descriptive and prescriptive ways that have not yet been fully explored for designing, then knitting, complex patterns. In particular, we generate knitting meta charts, i.e. abstract schemes, which admit different knitting charts according to the knitting techniques chosen. We thus produce new intricate and recursive patterns which in our opinion also exhibit a sense of artistry and beauty.

关键词： knitting charts formal grammars recursive algorithms Kolmogorov complexity knitting complexity

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A SINGULAR VALUE DECOMPOSITION UPDATING ALGORITHM FOR SUBSPACE TRACKING

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SIAM JOURNAL ON MATRIX ANALYSIS AND APPLICATIONS 1992年第4期13卷 1015-1038页

作者： MOONEN, M VANDOOREN, P VANDEWALLE, J BELGIAN NATL FUND SCI RES LOUVAIN BELGIUM UNIV ILLINOIS DEPT ELECT & COMP ENGN URBANA IL 61801 USA

In this paper, the well-known QR updating scheme is extended to a similar but more versatile and generally applicable scheme for updating the singular value decomposition (SVD). This is done by supplementing the QR updating with a Jacobi-type SVD procedure, where apparently only a few SVD steps after each QR update suffice in order to restore an acceptable approximation for the SVD. This then results in a reduced computational cost, comparable to the cost for merely QR updating. The usefulness of such an approximate updating scheme when applied to subspace tracking is examined. It is shown how an O(n2) SVD updating algorithm can restore an acceptable approximation at every stage, with a fairly small tracking error of approximately the time variation in O(n) time steps. Finally, an error analysis is performed, proving that the algorithm is stable, when supplemented with a Jacobi-type reorthogonalization procedure, which can easily be incorporated into the updating scheme.

关键词： SINGULAR VALUE DECOMPOSITION recursive algorithms

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Local Conditioning: Exact Message Passing for Cyclic Undirected Distributed Networks

Local Conditioning: Exact Message Passing for Cyclic Undirec...

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Future Technologies Conference (FTC)

作者： Reyes, Matthew G. Independent Researcher and Consultant Ann Arbor 48105 MI United States

ISBN: (纸本)9783030026837;9783030026820

This paper addresses practical implementation of summing out, expanding, and reordering of messages in Local Conditioning (LC) for undirected networks. In particular, incoming messages conditioned on potentially different subsets of the receiving node's relevant set must be expanded to be conditioned on this relevant set, then reordered so that corresponding columns of the conditioned matrices can be fused through element-wise multiplication. An outgoing message is then reduced by summing out loop cutset nodes that are upstream of the outgoing edge. The emphasis on implementation is the primary contribution over the theoretical justification of LC given in Fay et al. Nevertheless, the complexity of Local Conditioning in grid networks is still no better than that of Clustering.

关键词： Local Conditioning Belief Propagation Distributed Systems Message passing Cyclic networks recursive algorithms

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Incremental Frequency, Amplitude and Phase Tracker (IFAPT) for coherent demodulation over fast flat fading channels

Incremental Frequency, Amplitude and Phase Tracker (IFAPT) f...

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IEEE Information Theory Workshop

作者： Bar-David, I Elia, A Technion Israel Inst Technol Dept Elect Engn IL-32000 Haifa Israel

ISBN: (纸本)0780344081

IFAPT estimates the parameters of piece-wise linear approximation to assumed continuous narrow-band signals. Its simple, recursive nature enables direct interaction with recursive algorithms, such as the Viterbi and the BCJR in the APP SISO module, used for iteratively decoding concatenated codes. An augmented APP (A(2)P(2))-module, containing IFAPT and BCJR algorithms is here applied to iterative decoding serial concatenated convolutional codes under Rayleigh fading conditions, with diversity reception.

关键词： coherent demodulation Piecewise linear approximation flat fading channel recursive algorithms diversity reception recursiveness Fading (Conditioning) Incremental

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8th IEEE International Conference on Electron Devices and Solid State Circuit (EDSSC)

作者： Rassameyoungtong, Jade Srinonchat, Jakkree Rajamangala Univ Technol Dept Elect & Telecommun Engn Thanyaburi 12110 Rathumtani Thailand

ISBN: (纸本)9781467356961;9781467356947

The kalman filter is a recursive predictive filter that is based on the use of state space techniques and recursive algorithms. The advantage of kalman filter is, it estimates the state of dynamic system which can be disturbed by some noise. Thus this article presents the correlated noise reducing model using a kalman filter for speech vector quantization. The Q and R covariance constant parameters are investigated to provide the optimal performance with minimum noise of speech vector quantization signal. The results show that this model provides the minimum error as 1.0023 and 0.3622 for measurement error covariance and estimatation error covariance respectively.

关键词： kamal filter noise reducition Speech processing covariance constant recursive algorithms

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Multi-objective optimization of a plug flow reactor using a divide and conquer approach

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IFAC-PapersOnLine 2017年第1期50卷 8722-8727页

作者： Hashem I. Telen D. Nimmegeers P. Logist F. Van Impe J. KU Leuven Chemical Engineering Department BioTeC+ & OPTEC Gebroeders De Smetstraat 1 Gent 9000 Belgium

Lower profit margins and tighter environmental constraints push chemical companies to search for sustainable development and operation. To ensure sustainable development and operation in practice, multiple and conflicting objectives (e.g., maximize production vs. minimize energy consumption) typically have to be optimized simultaneously. The frame of multi-objective optimization allows to systematically propose improvements and evaluate trade-offs between different objectives. Solving a multi-objective optimization problem yields a set of solutions called the Pareto front, in which no improvement can be made in one objective without worsening another objective. The posteriori analysis of this set by a smart filter aims to keep only the significant solutions for the decision maker who is interested in a specific level of trade-offs. However, this strategy suffers from the large overhead of insignificant solutions produced in the original set. This situation makes applying this strategy to the complex multi-objective optimal control problems time consuming. In this paper, the smart filter by Mattson et al. (2004) is compared to a novel Divide and Conquer (D&C) algorithm to obtain a Pareto front with adaptive resolution for a case study of a plug flow reactor. The new algorithm depends on obtaining the Pareto front recursively while terminating the exploration of a Pareto front segment as soon as an insignificant point is found. It is shown that the D&C algorithm produces representations with similar quality to the smart filter with higher speed and a more intuitive trade-off oriented solution procedure. © 2017

关键词： Multi-objective optimisation Optimal control Process industry recursive algorithms

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