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A NEW TIME DOMAIN, MULTISTAGE PERMUTATION ALGORITHM

IEEE TRANSACTIONS ON INFORMATION THEORY 1990年第1期36卷 171-173页

作者： RAMANAN, SV JORDAN, HF SAUER, JR Optoelectronic Computing Systems Center University of Colorado Boulder Boulder CO USA

It is shown that a frame of N time slots can be arbitrarily permuted with 2log/sub 2/N-1 controlled exchange switches with associated delay elements. This is an improvement over previously known interconnection networks that require O(N) exchange elements. The proof utilizes the recursive algorithm of V.E. Benes (1965) and the time interchange properties of a particular configuration of a single exchange element. The architecture is especially applicable in optical systems, since optical exchange switches are among the simplest optical logic devices to build, are inherently very fast, and are the best developed, although expensive.

关键词： Interconnection networks recursive algorithms Optical Systems MULTISTAGE TIME-DOMAIN Switches optical logic delay element Switched systems Permutation

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Fast computation of the Bezout and Dixon resultant matrices

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JOURNAL OF SYMBOLIC COMPUTATION 2002年第1期33卷 13-29页

作者： Chionh, EW Zhang, M Goldman, RN Natl Univ Singapore Sch Comp Singapore 117543 Singapore Rice Univ Dept Comp Sci Houston TX 77005 USA

Efficient algorithms are derived for computing the entries of the Bezout resultant matrix for two univariate polynomials of degree n and for calculating the entries of the Dixon-Cayley resultant matrix for three bivariate polynomials of bidegree (m, n). Standard methods based on explicit formulas require O(n(3)) additions and multiplications to compute all the entries of the Bezout resultant matrix. Here we present a new recursive algorithm for computing these entries that uses only O(n(2)) additions and multiplications. The improvement is even more dramatic in the bivariate setting. Established techniques based on explicit formulas require O(m(4)n(4)) additions and multiplications to calculate all the entries of the Dixon-Cayley resultant matrix. In contrast, our recursive algorithm for computing these entries uses only O(m(2)n(3)) additions and multiplications. (C) 2002 Academic Press.

关键词： recursive algorithms Resultant Polynomial entry efficient algorithm

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On Pell partitions

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FIBONACCI QUARTERLY 2004年第4期42卷 348-352页

作者： Knopfmacher, A Robbins, N Univ Witwatersrand John Knopfmacher Ctr Applicable Anal & Number The Johannesburg South Africa San Francisco State Univ Dept Math San Francisco CA 94132 USA

Let Un denote the number of partitions of the natural number n, all of whose parts bi to {P-n,}- In this note, we present a recursive algorithm for computing Un. The techn used here are also applicable to other second order linear recurrences that have the pro] of being super-increasing, that is, where each term exceeds the sum of all its predecessoi [1], the second author solved the corresponding problem for the Fibonacci sequence.

关键词： Fibonacci sequence recursive algorithms partitions Denote Proline Writers PART Relapse Note Taking Natural number bismuth

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On some techniques for streaming data: A case study of Internet packet headers

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JOURNAL OF COMPUTATIONAL AND GRAPHICAL STATISTICS 2003年第4期12卷 893-914页

作者： Wegman, EJ Marchette, DJ George Mason Univ Ctr Computat Stat Fairfax VA 22030 USA USN Ctr Surface Warfare Dahlgren VA 22448 USA

We consider the implications of streaming data for data analysis and data mining. Streaming data are becoming widely available from a variety of sources. In our case we consider the implications arising from Internet traffic data. By implication, streaming data are unlikely to be time homogeneous so that standard statistical and data mining procedures do not necessarily apply. Because it is essentially impossible to store streaming data, we consider recursive algorithms, algorithms which are adaptive and discount the past and also algorithms that create finite pseudo-samples. We also suggest some evolutionary graphics procedures that are suitable for streaming data. We begin our discussion with a discussion of Internet traffic in order to give the reader some sense of the time and data scale and visual resolution needed for such problems.

关键词： evolutionary graphics exponential smoothing mixture models recursive algorithms recursive density estimation

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NORMAL COORDINATE EXPANSION OF THE WESS-ZUMINO-WITTEN MODEL

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EUROPHYSICS LETTERS 1988年第2期6卷 113-117页

作者： XI, ZM Center of Theoretical Physics CCAST (World Laboratory) Institute of Theoretical Physics Academia Sinica - P.O. Box 2735 Beijing China

The recursive algorithm of the normal coordinate expansion of the nonlinear sigma-model of Mukhi is extended. A simple background field expansion for the Wess-Zumino-Witten nonlinear sigma-model is presented. The general structure of itsn-th order term in the expansion is explicitly given. It is shown that this expansion is equivalent to the usual background field expansion in the matrix form of the chiral model.

关键词： normal coordinates recursive algorithms general structure Sigma model Expansion Equivalent

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The size of random fragmentation trees

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PROBABILITY THEORY AND RELATED FIELDS 2008年第3-4期142卷 399-442页

作者： Janson, Svante Neininger, Ralph Goethe Univ Frankfurt Dept Math & Comp Sci D-60054 Frankfurt Germany Uppsala Univ Dept Math S-75106 Uppsala Sweden

We consider the random fragmentation process introduced by Kolmogorov, where a particle having some mass is broken into pieces and the mass is distributed among the pieces at random in such a way that the proportions of the mass shared among different daughters are specified by some given probability distribution (the dislocation law);this is repeated recursively for all pieces. More precisely, we consider a version where the fragmentation stops when the mass of a fragment is below some given threshold, and we study the associated random tree. Dean and Majumdar found a phase transition for this process: the number of fragmentations is asymptotically normal for some dislocation laws but not for others, depending on the position of roots of a certain characteristic equation. This parallels the behavior of discrete analogues with various random trees that have been studied in computer science. We give rigorous proofs of this phase transition, and add further details. The proof uses the contraction method. We extend some previous results for recursive sequences of random variables to families of random variables with a continuous parameter;we believe that this extension has independent interest.

关键词： ARY SEARCH-TREES RANDOM-VARIABLES recursive algorithms SPLITTING INTERVALS DISTRIBUTIONS ASYMPTOTICS INVARIANCE PRINCIPLE THEOREMS SPACE

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On the contraction method with degenerate limit equation

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ANNALS OF PROBABILITY 2004年第3B期32卷 2838-2856页

作者： Neininger, R Rüschendorf, L Univ Frankfurt Dept Math D-60325 Frankfurt Germany Univ Freiburg Inst Math Stochast D-79104 Freiburg Germany

A class of random recursive sequences (Y-n) with slowly varying variances as arising for parameters of random trees or recursive algorithms X leads after normalizations to degenerate limit equations of the form X =(L) X. For nondegenerate limit equations the contraction method is a main tool to establish convergence of the scaled sequence to the "unique" solution of the limit equation. In this paper we develop an extension of the contraction method which allows us to derive limit theorems for parameters of algorithms and data structures with degenerate limit equation. In particular, we establish some new tools and a general convergence scheme, which transfers information on mean and variance into a central limit law (with normal limit). We also obtain a convergence rate result. For the proof we use selfdecomposability properties of the limit normal distribution which allow us to mimic the recursive sequence by an accompanying sequence in normal variables.

关键词： contraction method analysis of algorithms recurrence recursive algorithms divide-and-conquer algorithm random recursive structures Zolotarev metric

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recursive MOVING WINDOW DFT ALGORITHM

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IEEE TRANSACTIONS ON COMPUTERS 1990年第1期39卷 145-148页

作者： ARAVENA, JL Dept of Electr. & Comput. Eng. Louisiana State Univ. Baton Rouge LA USA Abstract Authors References Cited By Keywords Metrics Similar Download Citation Email Print Request Permissions

A recursive algorithm is presented for computing the discrete Fourier transform (DFT). The algorithm is developed for a moving-window-type processing. The computational structure is fully concurrent and allows a vectorized updating of the DFT. The total time required for the updating could be as low as that of only one multiplication and two additions, regardless of the number of points. A possible structure for executing the computations is developed, and possible enhancements are analyzed.

关键词： Moving recursive algorithms algorithms recursive as-cast structure

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recursive Implementations of the Schmidt-Kalman 'Consider' Filter

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JOURNAL OF THE ASTRONAUTICAL SCIENCES 2013年第3-4期60卷 672-685页

作者： Zanetti, Renato D'Souza, Christopher Charles Stark Draper Lab Vehicle Dynam & Controls 17629 El Camino RealSuite 470 Houston TX 77058 USA NASA Johnson Space Ctr Houston TX 77058 USA NASA GN & C Autonomous Flight Syst Branch Aerosci & Flight Mech Div Johnson Space Ctr EG6 Houston TX 77058 USA

One method to account for parameters errors in the Kalman filter is to 'consider' their effect in the so-called Schmidt-Kalman filter. This paper addresses issues that arise when implementing a consider Kalman filter as a real-time, recursive algorithm. A favorite implementation of the Kalman filter as an onboard navigation subsystem is the UDU formulation. A new way to implement a UDU Schmidt Kalman filter is proposed. The non-optimality of the recursive Schmidt-Kalman filter is also analyzed, and a modified algorithm is proposed to overcome this limitation.

关键词： recursive algorithms Filters recursive Kalman filters

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AN INVARIANT MEASURE APPROACH TO THE CONVERGENCE OF STOCHASTIC APPROXIMATIONS WITH STATE DEPENDENT NOISE

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SIAM JOURNAL ON CONTROL AND OPTIMIZATION 1984年第1期22卷 13-27页

作者： KUSHNER, HJ SHWARTZ, A BROWN UNIV DEPT APPL MATHPROVIDENCERI 02912

A new method is presented for quickly getting the ODE (ordinary differential equation) associated with the asymptotic properties of the stochastic approximation $X_{n + 1} = X_n + a_n f(X_n ,\zeta _n )$ (or the projected algorithm for the constrained problem). Either $a_n \to 0$, or $a_n $ can be constant, in which case the analysis is on the sequence obtained when $a \to 0$. The method requires that $\{ X_n ,\zeta _{n - 1} \} $ be Markov with a “Feller” transition function, but little else. The simplest result requires that if $X_n \equiv x$, the corresponding noise process $\{ \zeta _n (x),n \geqq 0\} $ have a unique invariant measure; but the “nonunique” case can also be treated. No mixing condition is required, nor the construction of averaged test functions, and $f(\cdot ,\cdot )$ need not be continuous. A detailed analysis of the way that $\{ \zeta _n \} $ varies with $\{ X_n \} $ is not required. For the class of sequences treated, the conditions seem easier to verify than for other methods. There are extensions to the non-Markov case. Two examples illustrate the power and ease of use of the approach. Aside from the advantages of the method in treating standard problems, it seems to be particularly useful for handling the type of iterative algorithms which arise in adaptive communication theory, where the dynamics are often discontinuous and the “noise” is often state-dependent due to the effects of feedback. If the noise $\{ \zeta _n \} $ is not “state-dependent,” then the Markov assumption can be dropped, and the method is even easier to use.

关键词： stochastic approximation recursive algorithms adaptive control

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