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1.
The length l of addition chains for z is shown to be bounded from below by log 2z+ log 2s( z)?2.13, where s( z) denotes the sum of the digits in the binary expansion of z. The proof given here will also hold for addition-subtraction chains if s( z) is replaced by an appropriate substitute. At first the proof is presented in a simplified version yielding the slightly weaker result l?log 2z+log 2s( z)?0 (log log s( z)). 相似文献
2.
An addition chain is a finite sequence of positive integers 1 = a
0 ≤ a
1 ≤ · · · ≤ a
r
= n with the property that for all i > 0 there exists a j, k with a
i
= a
j
+ a
k
and r ≥ i > j ≥ k ≥ 0. An optimal addition chain is one of shortest possible length r denoted l( n). A new algorithm for calculating optimal addition chains is described. This algorithm is far faster than the best known
methods when used to calculate ranges of optimal addition chains. When used for single values the algorithm is slower than
the best known methods but does not require the use of tables of pre-computed values. Hence it is suitable for calculating
optimal addition chains for point values above currently calculated chain limits. The lengths of all optimal addition chains
for n ≤ 2 32 were calculated and the conjecture that l(2 n) ≥ l( n) was disproved. Exact equality in the Scholz–Brauer conjecture l(2
n
− 1) = l( n) + n − 1 was confirmed for many new values. 相似文献
4.
Let ?(n) (respectively (n)) be the length of the shortest addition chain respectively addition/subtraction chain for n. We shall present several results on (n). In particular, we determine (n) for all n satisfying and show for all n satisfying , where is the extended sum of digits of n. These results are based on analogous results for ?(n) and on the following two inequalities: |n| ? 2 d?1F f+3 < 2 k?b and for a chain of length k = d + f + b with d doublings, f short steps, and b back steps for n. Moreover, we show that the difference (respectively ) can be made arbbitrarily large. In addition, we prove that and characterize the case . Finally, we determine , the k-dimensional generalization of , with the help of , the k-element generalization of . 相似文献
7.
Assume that we have two perspective images with known intrinsic parameters except for an unknown common focal length. It is a minimally constrained problem to find the relative orientation between the two images given six corresponding points. To this problem which to the best of our knowledge was unsolved we present an efficient solver. Through numerical experiments we demonstrate that the algorithm is correct, numerically stable and useful. The solutions are found through eigen-decomposition of a 15×15 matrix. The matrix itself is generated in closed form. 相似文献
9.
This paper considers approximating a given nth-order stable transfer matrix G(s) by an rth-order stable transfer matrix G r(s) in which n≫r, and where n is large. The Arnoldi process is used to generate a basis to a part of the controllability subspace associated with the realization of G(s), and a residual error is defined for any approximation in this subspace. We establish that minimizing the L ∞ norm of this residual error over the set of stable approximations leads to a 2-block distance problem. Finally, the solution of this distance problem is used to construct reduced-order approximate models. The behavior of the algorithms is illustrated with a simple example 相似文献
11.
We present a method for model reduction based on ideas from the behavioral theory of dissipative systems, in which the reduced order model is required to reproduce a subset of the set of trajectories of minimal dissipation of the original system. The passivity-preserving model reduction method of Antoulas (Syst Control Lett 54:361–374, 2005) and Sorensen (Syst Control Lett 54:347–360, 2005) is shown to be a particular case of this more general class of model reduction procedures. 相似文献
12.
In recent years several authors have investigated binary search trees with minimal internal path length. In this paper we propose relaxing the requirement of inserting all nodes on one level before going to the next level. This leads to a new class of binary search trees called ISA [ k] trees. We investigated the average locate cost per node, average shift cost per node, total insertion cost, and average successful search cost for ISA[ k] trees. We also present an insertion algorithm with associated predecessor and successor functions for ISA[ k] trees. For large binary search trees (over 160 nodes) our results suggest the use of ISA[2] or ISA[3] trees for best performance. 相似文献
14.
We discuss the simulation of M replications of a uniformizable Markov chain simultaneously and in parallel (the so-called parallel replicated approach). Distributed implementation on a number of processors and parallel SIMD implementation on massively parallel computers are described. We investigate various ways of inducing correlation across replications in order to reduce the variance of estimators obtained from the M replications. In particular, we consider the adaptation of Stratified Sampling, Latin Hypercube Sampling, and Rotation Sampling to our setting. These algorithms can be used in conjunction with the Standard Clock simulation of uniformized chains at distinct parameter values and can potentially sharpen multiple comparisons of systems in that setting. Our investigation is primarily motivated by this consideration. 相似文献
15.
A model reduction problem of certain large-scale Markov chains under an optimal criterion for Hankel-norm approximation is discussed. The multi-dimensional Markov chain under investigation is assumed to have a finite-dimensional stationary state-transition matrix, which is first reformulated as a multi-input/multi-output (MIMO) linear time-invariant (LT1) stochastic system. Consequently, the resulting large-scale MIMO LTI stochastic system has a closed-form best approximant in the Hankel-norm from a specified class of stable lower-dimensional MIMO LTI systems. 相似文献
16.
基于构造自正交码码树,研究由已知自正交码构造新自正交码的生成矩阵降维方法,采用贪婪策略和BFS算法,提出可行的降维算法。对GF(4)上码长20≤n≤30的自对偶码利用降维算法构造出其子码链及导出其L-链,进而得到45个较好参数达的量子码,其中7个改进了前人所得量子码的参数。 相似文献
17.
The present work deals with the inverse dynamics simulation of underactuated mechanical systems relying on servo constraints. The servo-constraint problem of discrete mechanical systems is governed by differential–algebraic equations (DAEs) with high index. We propose a new index reduction approach, which makes possible the stable numerical integration of the DAEs. The new method is developed in the framework of a specific crane formulation and facilitates a reduction from index five to index three and even to index one. Particular attention is placed on the special case in which the reduced index-1 formulation is purely algebraic. In this case the system at hand can be classified as differentially flat system. Both redundant coordinates and minimal coordinates can be employed within the newly developed approach. The success of the proposed method is demonstrated with two representative numerical examples. 相似文献
18.
Current image acquisition devices require tremendous amounts of storage for saving the data returned. This paper overcomes the latter drawback through proposing a colour reduction technique which first subdivides the image into patches, and then makes use of fuzzy c-means and fuzzy-logic-based inference systems, in order to cluster and reduce the number of the unique colours present in each patch, iteratively. The colours available in each patch are quantised, and the emergence of false edges is checked for, by means of the Sobel edge detection algorithm, so as to minimise the contour effect. At the compression stage, a methodology taking advantage of block-based singular value decomposition and wavelet difference reduction is adopted. Considering 35000 sample images from various databases, the proposed method outperforms centre cut, moment-preserving threshold, inter-colour correlation, generic K-means and quantisation by dimensionality reduction. 相似文献
20.
为提高信号频率估计精度和现有方法的普适性,提出一种基于频谱融合的多段同频等长信号的频率估计算法。设计相位差补偿因子克服分段信号相位不连续问题,以达到相位连续信号的频谱分析效果;建立搜索频率序列修正相位差补偿因子中的未知参数,并对分段信号频谱进行相位差补偿得到修正频谱矩阵;通过累积频谱抽取谱和修正频谱计算频谱相关序列并搜索最大值,其对应搜索频率即为该算法的频率估计值。数值仿真实验表明,基于该算法频率估计的均方根误差约为现有方法的1/4~2/3,较为接近Cramer-Rao下限。 相似文献
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