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An improved computational algorithm for finding the factorial

MATHEMATICAL NOTES 2008年第5-6期83卷 783-789页

作者： Ladikov, A. V. Moscow State Univ Railway Engn MIIT Moscow Russia

In the present paper, we consider a method for improving the computational algorithm for finding the factorials of integers;this method linearly accelerates the computations. We also present several algorithms effecti... 详细信息

关键词： computational algorithm factorial algorithm complexity

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Fractal image coding - achievements and prospects

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ANNALES DES TELECOMMUNICATIONS-ANNALS OF TELECOMMUNICATIONS 1998年第5-6期53卷 219-228页

作者： Popescu, DC CSIRO Div Math & Informat Sci Canberra ACT 2601 Australia

Fractal image coding is a relatively new technique of lossy image compression which exploits the piecewise self-similarity existing in an image. in this paper we present a survey of the achievements in the field We then focus our attention on a fundamental aspect of fractal coding - that concerning the nature of the transformations used in matching natural patterns. Through the analysis of a few models we try to suggest both the difficulties and the potential of this line of research.

关键词： image coding fractal system information compression algorithm complexity picture quality geometric transformation isometry

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A COMPUTATIONALLY EFFICIENT APPROXIMATION TO THE NEAREST NEIGHBOR INTERCHANGE METRIC

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JOURNAL OF CLASSIFICATION 1984年第1期1卷 93-124页

作者： BROWN, EK DAY, WHE MEM UNIV NEWFOUNDLAND DEPT COMP SCIST JOHNS A1C 5S7NEWFOUNDLANDCANADA

The nearest neighbor interchange (nni) metric is a distance measure providing a quantitative measure of dissimilarity between two unrooted binary trees with labeled leaves. The metric has a transparent definition in terms of a simple transformation of binary trees, but its use in nontrivial problems is usually prevented by the absence of a computationally efficient algorithm. Since recent attempts to discover such an algorithm continue to be unsuccessful, we address the complementary problem of designing an approximation to the nni metric. Such an approximation should be well-defined, efficient to compute, comprehensible to users, relevant to applications, and a close fit to the nni metric; the challenge, of course, is to compromise these objectives in such a way that the final design is acceptable to users with practical and theoretical orientations. We describe an approximation algorithm that appears to satisfy adequately these objectives. The algorithm requires O(n) space to compute dissimilarity between binary trees withn labeled leaves; it requires O(n logn) time for rooted trees and O(n ² logn) time for unrooted trees. To help the user interpret the dissimilarity measures based on this algorithm, we describe empirical distributions of dissimilarities between pairs of randomly selected trees for both rooted and unrooted cases.

关键词： algorithm complexity algorithm design Binary tree Crossover metric Dissimilarity measure Distance measure Hierarchical classification nni metric

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THE FAST SUBSAMPLED-UPDATING FAST TRANSVERSAL FILTER (FSU FTF) RLS algorithm

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ANNALES DES TELECOMMUNICATIONS-ANNALS OF TELECOMMUNICATIONS 1994年第7-8期49卷 407-413页

作者： SLOCK, DTM MAOUCHE, K 1. Institut Eurecom BP 193 F-06904 Sophia Antipolis Cedex France

We present a new fast algorithm for Recursive Least-Squares (RLS) adaptive filtering that uses displacement structure and subsampled updating. The FSU FTF algorithm is based on the Fast Transversal Filter (FTF) algorithm, which exploits the shift invariance that is present in the RLS adaptation of a FIR filter. The FTF algorithm is in essence the application of a rotation matrix to a set of filters and in that respect resembles the Levinson algorithm. In the subsampled updating approach, we accumulate the rotation matrices over some time interval before applying them to the filters. It turns out that the successive rotation matrices themselves can be obtained from a Schur type algorithm which, once properly initialized, does not require inner products. The various convolutions that thus appear in the algorithm are done using the Fast Fourier Transform (FFT). For relatively long filters, the computational complexity of the new algorithm is smaller than the one of the well-known LMS algorithm, rendering it especially suitable for applications such as acoustic echo cancellation.

关键词： FAST algorithm ADAPTIVE FILTERING FIR FILTER TRANSVERSE FILTER LEAST SQUARES METHOD UPDATING RECURSIVITY algorithm complexity

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PHASE-CORRECTIVE FILTER FOR UNDER-OPTIMUM EQUALIZERS

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ANNALES DES TELECOMMUNICATIONS-ANNALS OF TELECOMMUNICATIONS 1992年第9-10期47卷 359-369页

作者： WAUTIER, A DANY, JC MOUROT, C ALCATEL RADIOTEL F-92707 COLOMBESFRANCE

We propose a receiver structure intended for high bit rate transmissions. In order to ensure a good compromise between performance and complexity, the receiver is composed of a transversal phase-corrective filter followed by an equaliser, which takes only partially the channel impulse response into "count. We propose a non-iterative technique to adjust the filter tap coefficients, based on the cepstral properties of a minimum phase response. The performance of the filter is evaluated and shown by simulating a transmission system including a multipath mobile radio channel, the filter and a DFSE equaliser (decision feedback sequence estimator).

关键词： TRANSVERSE FILTER EQUALIZER, DIGITAL TRANSMISSION MULTIPATH PROPAGATION ADAPTIVE FILTER algorithm complexity PERFORMANCE EVALUATION CEPSTRUM

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FAST DISCRETE HARTLEY TRANSFORM

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ANNALES DES TELECOMMUNICATIONS-ANNALS OF TELECOMMUNICATIONS 1985年第9-10期40卷 477-480页

作者： PRADO, J 1.Département Systèmes et Communications Ecole Nationale Supérieure des Télécommunications 46 rue Barrault 75634 Paris Cedex 13

On présente un algorithme de calcul d’une transformation de Fourier discrète adaptée aux signaux réels. Cet algorithme permet un calcul sur place de la transformée et sa structure à base 4 ne nécessite pas de réordonnancement à chaque étage. De plus, il se prête bien à l’analyse spectrale (calcul de périodogramme) de signaux pondérés par des fenêtres de type Hamming.

关键词： Théorie signal Transformation mathématique Transformation discrète généralisée Transformation Fourier discrète Suite numérique Complexité algorithme Analyse spectrale Signal theory Mathematical transformation Generalized discrete transformation Discrete Fourier transform Numerical sequence algorithm complexity Spectral analysis

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A LINEAR APPLICATIVE SOLUTION FOR THE SET UNION PROBLEM

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INFORMATION PROCESSING LETTERS 1985年第1期20卷 43-45页

作者： MEIRA, SL UNIV FED PERNAMBUCO BR-50000 RECIFEPEBRAZIL

A linear applicative solution is presented for the Imperative Set Union problem. This problem is among those thought not to have a purely applicative solution of the same order of complexity as the best imperative solutions available. Without any programming tricks, it is shown that the Set Union, Intersection, and Difference problems do have applicative solutions comparable to the most widely known imperative versions. The complexity of the solution, or rather of one of the functions in it, is dependent upon the implementation's capability of destructively overwriting objects if that does not affect the referential transparency property of a purely applicative language. The methods presented might not work in all cases, but they clearly offer very efficient applicative solutions for many families of problems. The open issue is whether there exists a purely applicative solution of the same complexity for each best imperative algorithm known.

关键词： Applicative languages set union problem algorithm complexity KRC

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Pedestrian Detection algorithms Based on an Analysis of the Autocorrelation Function of a Seismic Signal

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OPTOELECTRONICS INSTRUMENTATION AND DATA PROCESSING 2011年第2期47卷 124-129页

作者： Alyamkin, S. A. Eremenko, S. I. Uniscan Co Ul Arbuzova 4-26 Novosibirsk 630117 Russia

A pedestrian detection algorithm based on an analysis of the autocorrelation function of a seismic signal is proposed. The efficiency of this method in terms of detection and false alarm probabilities is shown. Approaches to reducing the complexity of the proposed algorithm are considered. A comparative study is made of the effects of the point sampling frequency and the method of calculating the autocorrelation function on the performance and complexity of the pedestrian detection algorithm.

关键词： seismic monitoring systems pedestrian detection autocorrelation function algorithm complexity

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OPTIMUM SOFT-DECISION DECODING OF LINEAR BLOCK-CODES .1. SIMPLIFIED TRELLIS DECODING

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ANNALES DES TELECOMMUNICATIONS-ANNALS OF TELECOMMUNICATIONS 1983年第11-1期38卷 443-459页

作者： BATTAIL, G Département Systèmes et Communications Ecole Nationale Supérieure des Télécommunications 46 rue Barrault 75634 Paris Cedex 13

Analyse On envisage le décodage pondéré, à vraisemblance maximale mot par mot, des codes q-aires linéaires en blocs. Tous les mots d’un tel code sont représentés par un diagramme en treillis, précisément défini grâce à la représentation du code par un polynôme à plusieurs indéterminées. On définit en fonction des probabilités a priori une « cote » associée aux chemins en les nœuds du treillis, qui est une fonction non croissante du niveau de nœud et telle que le mot qui atteint la plus grande cote au dernier niveau de nœud (cote finale) est le meilleur pour le critère de vraisemblance maximale. Le décodage peut alors utiliser l’algorithme de Viterbi mais, si la cote finale d’un chemin particulier est connue, les nœuds du treillis de cote supérieure peuvent seuls appartenir au meilleur chemin. De plus, dès que l’on trouve un chemin meilleur que le chemin initialement considéré, sa cote finale sert de nouveau seuil pour la cote des nœuds, au-dessous duquel il n’y a plus à en tenir compte. Le seuil initial adopté est la cote finale du chemin spécifié par le résultat de la décision ferme sur les k premiers symboles, k étant la dimension du code. On montre de plus que son calcul fait intervenir celui du syndrome. On examine la stratégie d’exploration des autres chemins. On montre qu’un classement des symboles par fiabilité décroissante rend minimal le volume de calcul nécessaire en moyenne. Pour terminer, des moyens de simplifier davantage au détriment de l’optimalité sont brièvement décrits.

关键词： Block code Linear code Non binary code Optimal decoding Trellis Maximum likelihood Viterbi decoding Simplification algorithm complexity Weighting

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Time-domain analysis methodology for large-scale RLC circuits and its applications

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Science in China(Series F) 2006年第5期49卷 665-680页

作者： LUO Zuying CAI Yici Sheldon X.-D Tan HONG Xianlong WANG Xiaoyi PAN Zhu FU Jingjing Department of Computer Science and Technology Tsinghua University Beijing 100084 China College of Information Science and Technology Beijing Normal University Beijing 100875 China Department of Electrical Engineering University of California at Riverside Riverside CA92521 USA

With soaring work frequency and decreasing feature sizes, VLSI circuits with RLC parasitic components are more like analog circuits and should be carefully analyzed in physical design. However, the number of extracted RLC components is typically too large to be analyzed efficiently by using present analog circuit simulators like SPICE. In order to speedup the simulations without error penalty, this paper proposes a novel methodology to compress the time-descritized circuits resulted from numerical integration approximation at every time step. The main contribution of the methodology is the efficient structure-level compression of DC circuits containing many current sources, which is an important complement to present circuit analysis theory. The methodology consists of the following parts： 1） An approach is proposed to delete all intermediate nodes of RL branches. 2） An efficient approach is proposed to compress and back-solve parallel and serial branches so that it is error-free and of linear complexity to analyze circuits of tree topology. 3） The Y to πtransformation method is used to error-free reduce and back-solve the intermediate nodes of ladder circuits with the linear complexity. Thus, the whole simulation method is very accurate and of linear complexity to analyze circuits of chain topology. Based on the methodology, we propose several novel algorithms for efficiently solving RLC-model transient power/ground （P/G） networks. Among them, EQU-ADI algorithm of linear-complexity is proposed to solve RLC P/G networks with mesh-tree or mesh-chain topologies. Experimental results show that the proposed method is at least two orders of magnitude faster than SPICE while it can scale linearly in both time- and memory-complexity to solve very large P/G networks.

关键词： RLC circuits analog circuit analysis time-domain analysis PIG networks algorithm complexity

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