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M. Andrews 《Computers & Mathematics with Applications》1981,7(6):503-508
This paper is a continuation of a study of numerical software for evaluating elementary functions in a microcomputer environment. Here we describe three algorithms for evaluation of the exponential function that are based on rationals, polynomials and coarse table look-up, respectively. Focus is on the design of fast algorithms that preserve full machine precision in small scale machines which use truncated binary fixed point arithmetic with at most a sixteen-bit wordlength. Included in the paper is a comparison of the performance of these algorithms implemented in two contemporary microcomputers. 相似文献
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B. Iannazzo 《Calcolo》2003,40(4):273-283
We revisit recent algorithms for computing matrix square roots and relate them to Newton iteration. New iterations are derived and a stability analysis is performed. A suitable scaling of an algorithm based on cyclic reduction is introduced, which removes the slow convergence of this iteration encountered in certain cases. 相似文献
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Floating-point support has become a mandatory feature of new microprocessors due to the prevalence of business, technical, and recreational applications that use these operations. Spreadsheets, CAD tools, and games, for instance, typically feature floating-point-intensive code. Over the past few years, the leading architectures have incorporated several generations of floating-point units (FPUs). However, while addition and multiplication implementations have become increasingly efficient, support for division and square root has remained uneven. The design community has reached no consensus on the type of algorithm to use for these two functions, and quality and performance of the implementations vary widely. This situation originates in skepticism about the importance of division and square root and an insufficient understanding of the design alternatives. Quantifying what constitutes good performance is challenging. One rule thumb, for example, states that the latency of division should be three times that of multiplication; this figure is based on division frequencies in a selection of typical scientific applications. Even if we accept this doctrine at face value, implementing division-and square root-involves much more than relative latencies. We must also consider area, throughput, complexity, and the interaction with other operations. This article explores the various trade-offs involved and illuminates the consequences of different design choices, thus enabling designers to make informed decisions 相似文献
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Discrete square root filtering: A survey of current techniques 总被引:1,自引:0,他引:1
The conventional Kalman approach to discrete filtering involves propagation of a state estimate and an error covariance matrix from stage to stage. Alternate recursive relationships have been developed to propagate a state estimate and a square root error covariance instead. Although equivalent algebraically to the conventional approach, the square root filters exhibit improved numerical characteristics, particularly in ill-conditioned problems. In this paper, current techniques in square root filtering are surveyed and related by applying a duality association. Four efficient square root implementations are suggested, and compared with three common conventional implementations in terms of computational complexity and precision. The square root computational burden should not exceed the conventional by more than 50 percent in most practical problems. An examination of numerical conditioning predicts that the square root approach can yield twice the effective precision of the conventional filter in ill-conditioned problems. This prediction is verified in two examples. The excellent numerical characteristics and reasonable computation requirements of the square root approach make it a viable alternative to the conventional filter in many applications, particularly when computer word length is limited, or the estimation problem is badly conditioned. 相似文献
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A new efficient biorthogonal wavelet analysis based on the principal square root of subdivision is proposed in the paper by using the lifting scheme. Since the principal square root of subdivision is of the slowest topological refinement among the traditional triangular subdivisions, the multiresolution analysis based on the principal square root of subdivision is more balanced than the existing wavelet analyses on triangular meshes, and accordingly offers more levels of detail for processing polygonal models. In order to optimize the multiresolution analysis process, the new wavelets, no matter whether they are interior or on boundaries, are orthogonalized with the local scaling functions based on a discrete inner product with subdivision masks. Because the wavelet analysis and synthesis algorithms are actually composed of a series of local lifting operations, they can be performed in linear time. The experiments demonstrate the efficiency and stability of the wavelet analysis for both closed and open triangular meshes with principal square root of subdivision connectivity. The principal square root of -subdivision-based biorthogonal wavelets can be used in many applications such as progressive transmission, shape approximation, multiresolution editing and rendering of 3D geometric models. 相似文献
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Square root is an operation performed by the hardware in recent generations of processors. The hardware implementation of the square root operation is achieved by different means. One of the popular methods is the non-restoring algorithm. In this paper, the classical non-restoring array structure is improved in order to simplify the circuit. This reduction is done by eliminating a number of circuit elements without any loss in the precision of the square root or the remainder. For a 64-bit non-restoring circuit the area of the suggested circuit is about 44% smaller than that of a conventional non-restoring array circuit. Furthermore, in order to create an environment for modular design of the non-restoring square root circuit, a number of modules are suggested. Using these modules it is possible to construct any square root circuit with an arbitrary number of input bits. The suggested methodology results in an expandable design with reduced-area. Analytical and simulation results show that the delay of the proposed circuit, for a 64-bit radicand, is 80% less than that of a conventional non-restoring array circuit. 相似文献
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《Automatic Control, IEEE Transactions on》1990,35(12):1293-1298
The maximum likelihood parameter estimation algorithm is known to provide optimal estimates for linear time-invariant dynamic systems. However, the algorithm is computationally expensive and requires evaluations of the gradient of a log likelihood function and the Fisher information matrix. By using the square-root information filter, a numerically reliable algorithm to compute the required gradient and the Fisher information matrix is developed. The algorithm is a significant improvement over the methods based on the conventional Kalman filter. The square-root information filter relies on the use of orthogonal transformations that are well known for numerical reliability. This algorithm can be extended to real-time system identification and adaptive control 相似文献
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《国际计算机数学杂志》2012,89(3):297-302
In this paper an iterative algorithm has been presented for calculating the square root of a real number with arbitrary order of convergence using formulae derived by applying binomial theorem. The primary objective is to reduce the number of division operations required. 相似文献
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Nagwa Sherif 《Computing》1991,46(4):295-305
The inverse square root of a matrix plays a role in the computation of an optimal symmetric orthogonalization of a set of vectors. We suggest two iterative techniques to compute an inverse square root of a given matrix. The two schemes are analyzed and their numerical stability properties are investigated. 相似文献
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Gerald J. Bierman 《Automatica》1974,10(2):147-158
Square-root information estimation algorithms are immensely important estimation analysis tools that are not sufficiently well understood nor adequately exploited. In an endeavor to rectify this state of affairs an expository derivation of the square-root information filter/smoother is given. It is based on the recursive least-squares method and is easier to grasp, interpret and generalize than are the dynamic programming arguments previously used. Backward smoothing algorithms, both square-root and covariance recursions, are derived as direct and consequences of the method. A comparison of smoothing algorithms indicates that those presented in this paper are the most efficient. Partitioning the results to separate bias parameters provides further computational economies and reduction of storage requirements.The principal objective of this paper is to inspire greater utilization of square-root estimation algorithms. Arguments supporting this thesis are the new least-squares filter/smoother derivations, enhanced numerical accuracy, reduced computation, and lower storage requirements. 相似文献
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基于定点DSP的浮点开平方算法的实现 总被引:2,自引:3,他引:2
本文提出了基于TMS320C2XX定点DSP的浮点开平方算法,给出了实现方法及程序清单,实践证明该方法具有精度高,运算速度快、程序简单等特点。 相似文献
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Abstract: The increasing popularity of expert systems has led to a demand to apply expert systems technology in a wide variety of computing environments. As a result, various efforts have been made to implement expert systems on microcomputers. This article reviews some of the ongoing work on tools for the development of microcomputer-based expert systems. Some specific application areas are noted, and a brief discussion of the advantages and disadvantages of implementing expert systems on microcomputers is presented. 相似文献
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Adam Strzeboński 《Journal of Symbolic Computation》2012,47(3):282-314
We present a real root isolation procedure for univariate functions obtained by composition and rational operations from exp,log,arctan and real constants. The procedure was first introduced for exp-log functions in Strzeboński (2008). Here we extend the procedure to exp-log-arctan functions, describe computation with elementary constants in detail and discuss the complexity of the root isolation procedure for the general exp-log-arctan case as well as for the special case of sparse polynomials. We discuss implementation of the procedure and present empirical results. 相似文献