Recursive Algorithm For Computation Research Articles

Fast computation of Legendre moments of polyhedra

The three-dimensional (3D) orthogonal moments are an efficient tool for object reconstruction and 3D image analysis. However, until now, 3D orthogonal moments have not been analysed in detail from the point of view of reducing the computational complexity. In this paper, we present a recursive algorithm for fast computation of Legendre moments of polyhedra. First, a Gaussian theorem is employed to transform the volume integral into a surface one. The double integral can then be deduced from the simple integral by a Green's theorem. Finally, the recursive relationship is investigated. As one can see, the proposed method decreases the computational complexity tremendously.

Moment computation of lumped and distributed coupled RC trees with application to delay and crosstalk estimation

In today's deep submicrometer technology the coupling capacitances among individual on-chip RC trees have an essential effect on the signal delay and crosstalk, and the interconnects should be modeled as coupled RC trees. In this paper we provide simple exact explicit formulas for the Elmore delay and higher order voltage moments and a linear order recursive algorithm for the voltage moment computation for lumped and distributed coupled RC trees. By using the formulas and algorithms, the moment-matching method can be efficiently implemented to deal with delay and crosstalk estimation, model order reduction, and optimal design of interconnects. As an application of the algorithm, we provide a new efficient and accurate model for crosstalk estimation in coupled RC trees. Simulation results show it works better than existing methods.

FUZZY PREDICTIVE CONTROL OF UNCERTAIN CHAOTIC SYSTEMS USING TIME SERIES

In this paper, a simple fuzzy logic based intelligent mechanism is developed for predicting and controlling a chaotic system to a desired target, using only input–output data obtained from the unknown (or uncertain) underlying chaotic system. In the chaos prediction phase, a fuzzy system approach incorporating with Gaussian type of fuzzy membership functions is used. Only system input–output data are needed for prediction, and a recursive least-squares computational algorithm is employed for the calculation. In the controller design phase, the Lyapunov stability criterion is used, which forms the basis of the main design principle. Some simulation results on the chaotic Sin map and Hénon map are given, for both prediction and control, to illustrate the effectiveness and control performance of the proposed method.

Suboptimal Kalman filtering for linear systems with Gaussian-sum type of noise

This paper develops several suboptimal filtering algorithms for discrete-time linear systems that have state and/or measurement noise of the Gaussian-sum type. These new computational schemes are modifications and generalizations of the well-known algorithms of Sorenson and Alspach and of Masreliez. Under the common minimum mean square estimation criterion, these new schemes are derived as recursive computational algorithms. Monte Carlo simulations have shown that these new filtering algorithms significantly improve the computational efficiency and/or filtering performance of the existing algorithms.

RECURSIVE COMPUTATION OF THE PARAMETERS OF PERIODIC AUTOREGRESSIVE MOVING‐AVERAGE PROCESSES

Abstract. An algorithm for recursive computation of the parameters of periodic autoregressive moving‐average (ARMA) processes is given. It also provides recursions for stationary multivariate ARMA processes. A procedure for simultaneous estimation of the order and the parameters of a periodic ARMA process is outlined.

Constrained many-to-one string editing with memory

A new constrained edit distance between an ordered set of input strings and a single output string is proposed, where all the strings are over a finite alphabet. Editing transformation includes deletion of symbols from the input strings, combination of the decimated input strings by a function with memory, and substitution and insertion of symbols in the combination string. Constraints are related to the total number of edit operations and to the maximum numbers of consecutive deletions and insertions. A recursive algorithm for efficient computation of the constrained edit distance is derived and its computational complexity is determined. Potential applications in cryptanalysis of shift-register-based stream ciphers and in decoding for parallel communication channels with synchronization errors are also discussed.

Determination of mechanical spectra from experimental responses

A recursive computer algorithm was developed which generates line spectra from experimental response functions. The method allows storing information on the mechanical properties of polymeric materials in a convenient way. The algorithm also interconverts between relaxation and retardation spectra. From the spectra, any desired response function can then be recovered. The algorithm essentially utilizes the fact that the kernel functions resemble step functions. Slightly different codes are used for each kernel function. The appearance of negative relaxation or retardation lines is obviated. Mathematically such lines would be acceptable, and they do not seriously affect reconstruction of responses within relaxation or retardation behavior. However, they would seriously interfere with interconversion between the two types of behavior, and they would also pose problems in the interpretation of the spectra.

Generating line spectra from experimental responses. Part I: Relaxation modulus and creep compliance

We describe a recursive computer algorithm which generates line spectra from relaxation modulus or creep compliance data without producing negative spectrum lines. We apply the algorithm here to data read from mathematical models for the relaxation modulus. Since these data were thus free of the usual experimental error, we could use a relatively simple form of the basic algorithm that is applicable also to smoothed data. The spectra faithfully reproduced the input functions and may serve for data storage as well as for predicting other experimental responses.

A new formulation of Q-Markov covariance equivalent realization

The Q-Markov Covariance Equivalent Realization ( Q-Markov Cover) is a state space realization which matches the first Q Markov parameters and covariance parameters of a system. King, Desai, and Skelton [5] developed a generalized approach to generate Q-Markov Covers. Desai and Skelton [3] presented a recursive computational algorithm for generating Q-Markov Covers when Q is very large. Based on the works of the above two papers, we developed a new formula for generating Q-Markov Covers, and also an algorithm to compute them when Q is very large. The new formula has been applied for model identification of large flexible structures by Liu and Skelton [6–8]. Compared with previously developed formulas and algorithms, the new formula and algorithm are relatively straightforward and easy to program. This formula may simplify the further analytical study of Q-Markov Covers and its application to system identification.

Recursive computational algorithms for a set of block pulse operational matrices

A set of integral operational matrices, which are superior to the conventional and generalized integral operational matrices in the identification of time-varying linear systems via block pulse functions, can be calculated efficiently by the new recursive computational algorithms which are proposed in this paper. As the basis of these algorithms, the constant difference properties of entries of the set of operational matrices are proved. And as the advantage of these algorithms, the reduction of their computational size is discussed. The proposed algorithms are especially useful when the number of block pulses is large in realistic applications of the block pulse function method.

An algorithm for efficient computation of dynamics of robotic manipulators

AbstractThis article presents a recursive algorithm for computation of dynamics of robot manipulators using the concepts of “augmented body” and “barycenter.” This efficient algorithm is proposed for real‐time control. The proposed method of computation is based on Newton‐Euler formalism, and it can be applied to any rigid‐link manipulator with open‐loop kinematic chains with revolute and/or prismatic joints. The computational efficiency of the proposed method is compared with other published methods.

Limiting tail behaviour of some discrete compound distributions

This paper gives an elementary derivation of asymptotic estimates of the probability function, tail, and stop-loss premium of some discrete compound distributions which have been found to be of use in insurance claims modelling. These estimates provide insight into the distributional form, and often complement recursive computational algorithms which are cumbersome to apply in the right tail of the distribution. Some practical aspects of the use of these formulae are discussed.

Efficient computation of two-dimensional Gaussian windows

Kaiser (1987) described a fast recursive algorithm for computation of equidistant samples of a one-dimensional Gaussian function requiring only two multiplications per sampling point. We show that the algorithm remains valid for two-dimensional Gaussian windows and discuss its application to specific computer vision problems.

Prediction of satellite motions in the Earth's gravitational field with axial symmetry by the KS regularized theory

In this paper, economical and stable recurrence formulae for the Earth's zonal potential and its gradient for the KS regularized theory will be established for any numberN of the zonal harmonic coefficient. A general recursive computational algorithm based on these formulae is also established for the initial value problem of the KS theory for the prediction of artificial satellites in the Earth's gravitational field with axial symmetry. Applications of the algorithm for the problem of the final state prediction are illustrated by numerical examples of three test orbits each for two geopotential models corresponding toN=2 andN=36. A final state of any desired accuracy is obtained for each case study, a result which shows the flexibility of the algorithm.

Prediction of satellites in Earth's gravitational field with axial symmetry using Burdet's regularized theory

In this paper, economical and stable recurrence formulae for the Earth's zonal potential and its gradient for Burdet's regularized theory will be established for any number N of the zonal harmonic coefficients. A general recursive computational algorithm based on these formulae is also established for the initial value problem of Burdet oscillator for the prediction of artificial satellites in the Earth's gravitational field with axial symmetry. Applications of the algorithm for the problem of the final state prediction are illustrated by numerical examples of three test orbits each for two geopotential models corresponding to N = 2 and N = 36. A final state of any desired accuracy is obtained for each case study, a result which shows the flexibility of the algorithm.

A recursive computer algorithm for determining joint probability inventory distributions

Most reorder point inventory models have been characterized by either variable demands or variable lead times. Commonly used distributions that have been used to represent both demand and lead-time variation have included the Poisson, normal and negative exponential functions. When both demand and lead time are variable, the complexity of constructing a joint distribution to represent the lead-time demand impedes the use of traditional models by practitioners. Practitioners are more likely to use discrete probability distributions to represent both demand and lead-time variation. This paper presents a computer algorithm to facilitate the construction of joint probability distributions that represent the lead-time demand. Component distributions for both demand and lead-time variations are assumed to be discrete. The PASCAL computer model facilitates the construction of joint distributions for numbers of demand and lead-time alternatives too large to permit distribution construction by traditional, manual methods.

Recursive computational algorithm for the generalized block-pulse operational matrix

A new recursive computational algorithm for evaluating the entries in the generalized block-pulse matrix is derived in this paper. The Stirling number and a new extended theorem are used to prove the constant difference property of the entries of the generalized block-pulse operational matrix. A recursive algorithm can then be obtained. The reduction of computing effort and associated errors is very significant when the number of computing intervals is realistically large. In comparison with the previous recursive algorithm for repeated integral operations, this new algorithm specifically addresses evaluation of the matrix entries, which, as is well known, can then be applied to evaluate the effect of multiple integrations without the need for repeated applications of the conventional block-pulse function,

Computation of the exact information matrix of Gaussian time series with stationary random components

The paper presents an algorithm for efficient recursive computation of the Fisher information matrix of Gaussian time series whose random components are stationary, and whose means and covariances are functions of a parameter vector. The algorithm is first developed in a general framework and then specialized to the case of autoregressive moving-average processes, with possible additive white noise. The asymptotic behavior of the algorithm is explored and a termination criterion is derived. Finally, the algorithm is used to demonstrate the behavior of the exact Cramer-Rao bound (for unbiased estimates) for some ARMA processes, as a function of the number of data points. It is shown that for processes with zeros near the unit circle and short data records, the exact Cramer-Rao bound differs dramatically from its common approximation based on asymptotic theory.

Solutions of integral equations via modified Laguerre polynomials

The Laguerre polynomial function is modified with an additional parameter and is applied to solve integral equations. First, the convolution of two modified Laguerre polynomials is developed. The dependent variables in the integral equation are assumed to be expressed by a modified Laguerre polynomial series. A set of algebraic equations is obtained from the integral equation. A recursive computational algorithm is employed to calculate the expansion coefficients. Examples are given, the results obtained from the modified Laguerre polynomials being much better than from the conventional Laguerre polynomials.

Solutions of integral equations via modified Laguerre polynomials

The Laguerre polynomial function is modified with an additional parameter and is applied to solve integral equations. First, the convolution of two modified Laguerre polynomials is developed. The dependent variables in the integral equation are assumed to be expressed by a modified Laguerre polynomial series. A set of algebraic equations is obtained from the integral equation. A recursive computational algorithm is employed to calculate the expansion coefficients. Examples are given, the results obtained from the modified Laguerre polynomials being much better than from the conventional Laguerre polynomials.