New recursive algorithm for matrix inversion

To reduce the computational complexity of matrix inversion, which is the majority of processing in many practical applications, two numerically efficient recursive algorithms （called algorithms I and II, respectively） are presented. Algorithm I is used to calculate the inverse of such a matrix, whose leading principal minors are all nonzero. Algorithm II, whereby, the inverse of an arbitrary nonsingular matrix can be evaluated is derived via improving the algorithm I. The implementation, for algorithm II or I, involves matrix-vector multiplications and vector outer products. These operations are computationally fast and highly parallelizable. MATLAB simulations show that both recursive algorithms are valid.

Fast recursive algorithm for two-dimensional Tsallis entropy thresholding method

Recently, a two-dimensional （2-D） Tsallis entropy thresholding method has been proposed as a new method for image segmentation. But the computation complexity of 2-D Tsallis entropy is very large and becomes an obstacle to real time image processing systems. A fast recursive algorithm for 2-D Tsallis entropy thresholding is proposed. The key variables involved in calculating 2-D Tsallis entropy are written in recursive form. Thus, many repeating calculations are avoided and the computation complexity reduces to O（L2） from O（L4）. The effectiveness of the proposed algorithm is illustrated by experimental results.

A RECURSIVE ALGORITHM AND ITS CONVERGENCE FOR PARAMETER ESTIMATION OF CONVOLUTION MODEL

In this article, the problem on the estimation of the convolution model parameters is considered. The recursive algorithm for estimating model parameters is introduced from the orthogonal procedure of the data, the convergence of this algorithm is theoretically discussed, and a sufficient condition for the convergence criterion of the orthogonal procedure is given. According to this condition, the recursive algorithm is convergent to model wavelet A- = （1, α1,..., αq）.

REESSE Unified Recursive Algorithm for Solving Three Computational Problems

Different from the extended Euclidean algorithm which can compute directly only the multiplicative inverse of an element in Zm^＊ and the greatest common divisor of two integers, a recursive algorithm called REESSE is designed by the authors, which can not only seek directly the multiplicative inverse and the greatest common divisor, but also solve directly a simple congruence for general solutions. This paper presents the definition and the two valuable properties of a simple congruence, analyzes in detail the reduction and recursion process of solving simple congruences, induces the recursive formula for solving simple congruences, and describes formally and implements in C language the recursive algorithm. At last, the paper compares REESSE with the extended Euclidean algorithm in thought, applicability and time complexity.

Recursive Algorithm Based Reliability Analysis of Multiphase Satellite Systems with Propagated Failures

Modern satellite systems are generally designed to fulfill multiphase-missions. Component /subsystem redundancies are commonly used to achieve high reliability and long life of modern satellite systems. These characteristics have leaded to a critical issue of reliability analysis of satellites that is how to deal with the reliability analysis with multiphase-missions and propagated failures of redundant components. Traditional methods based on the binary decision diagram( BDD) can hardly cope with these issues efficiently. Accordingly, a recursive algorithm method was introduced to facilitate the reliability analysis of satellites. This method was specified for the analysis of static fault tree and it was implemented by generating combination of component failures and carrying out a backward recursive algorithm. The effectiveness of the proposed method was demonstrated through the reliability analysis of a multiphase satellite system with propagated failures.The major advantage of the proposed method is that it does not need composition of BDD and its computational process is automated.

A Recursive Algorithm on Rational Interpolation

In this paper we introduce a so called C-Matrix w.r.t a rational interpolation problem and study the relationship between the unattainable points and C-Matrix. Finally, we present a recursive algorithm on rational interpolation.

Recursive algorithm and accurate computation of dyadic Green's functions for stratified uniaxial anisotropic media

A recursive algorithm is adopted for the computation of dyadic Green＇s functions in three-dimensional stratified uniaxial anisotropic media with arbitrary number of layers. Three linear equation groups for computing the coefficients of the Sommerfeld integrals are obtained according to the continuity condition of electric and magnetic fields across the interface between different layers, which are in correspondence with the TM wave produced by a vertical unit electric dipole and the TE or TM wave produced by a horizontal unit electric dipole, respectively. All the linear equation groups can be solved via the recursive algorithm. The dyadic Green＇s functions with source point and field point being in any layer can be conveniently obtained by merely changing the position of the elements within the source term of the linear equation groups. The problem of singularities occurring in the Sommerfeld integrals is efficiently solved by deforming the integration path in the complex plane. The expression of the dyadic Green＇s functions provided by this paper is terse in form and is easy to be programmed, and it does not overflow. Theoretical analysis and numerical examples show the accuracy and effectivity of the algorithm.

CONVERGENCE AND STABILITY OF RECURSIVE DAMPED LEAST SQUARE ALGORITHM

The recursive least square is widely used in parameter identification. But if is easy to bring about the phenomena of parameters burst-off. A convergence analysis of a more stable identification algorithm-recursive damped least square is proposed. This is done by normalizing the measurement vector entering into the identification algorithm. rt is shown that the parametric distance converges to a zero mean random variable. It is also shown that under persistent excitation condition, the condition number of the adaptation gain matrix is bounded, and the variance of the parametric distance is bounded.

Performance of a recursive algorithm for polynomial predistorter design

In this article, based on least square estimation, a recursive algorithm for indirect learning structure predistorter is introduced. Simulation results show that of all polynomial predistorter nonlinear terms, higher-order （higher than 7th-order） nonlinear terms are so minor that they can be omitted in practical predistorter design. So, it is unnecessary to construct predistorter with higher-order polynomials, and the algorithm will always be stable. Further results show that even when 15th-order polynomial model is used, the algorithm is convergent after 10 iterations, and it can improve out-band spectrum of 20 MHz bandwidth signal by 64 dB, with a 1.2×10^11 matrix condition number.

Reflected-intensity distribution of angle-tuned thin film filter based on frequency recursive algorithm

For a three-port angle-tuned thin film filter, the characteristic of reflected-port is very important to reflect multiple wavelengths spectrum. As the filter is in tilted incidence, the reflected-facula broadens and the refiectivity decreases. In this paper, we proposed a frequency recursive algorithm based on fast Fourier transform and Fresnel formula. The reflected-intensity distribution of the narrow- band filter from normal incidence to 40~ tilted incidence was simulated by this frequency recursive algorithm. Meanwhile, the beam field experiments were accordingly performed in this study. Compared with the traditional beam spatial superposition method, the frequency recur- sive algorithm is more efficient and precise in calculating the reflectivity of the reflected beam, suggesting the frequency recursive algorithm may be more helpful for fabricating the three-port tunable thin film filter.

Recursive algorithm for the two-stage EFOP estimation method

A recursive algorithm for the two-stage empirical frequency-domain optimal parameter （EFOP） estimation method was proposed. The EFOP method was a novel system identification method for Black-box models that combines time-domain estimation and frequency-domain estimation. It has improved anti-disturbance performance, and could precisely identify models with fewer sample numbers. The two- stage EFOP method based on the boot-strap technique was generally suitable for Black-box models, but it was an iterative method and takes too much computation work so that it did not work well online. A recursive algorithm was proposed for dis- turbed stochastic systems. Some simulation examples are included to demonstrate the validity of the new method.

Minimal cut-based recursive decomposition algorithm for seismic reliability evaluation of lifeline networks

In this paper, a new probabilistic analytical approach, the minimal cut-based recursive decomposition algorithm （MCRDA）, is presented to evaluate the seismic reliability of large-scale lifeline systems. Based on the minimal cut searching algorithm, the approach calculates the disjoint minimal cuts one by one using the basic procedure of the recursive decomposition method. At the same time, the process obtains the disjoint minimal paths of the system. In order to improve the computation efficiency, probabilistic inequality is used to calculate a solution that satisfies the prescribed error bound. A series of case studies show that MCRDA converges rapidly when the edges of the systems have low reliabilities. Therefore, the approach can be used to evaluate large-scale lifeline systems subjected to strong seismic wave excitation.

An improved cut-based recursive decomposition algorithm for reliability analysis of networks

In this paper, an improved cut-based recursive decomposition algorithm is proposed for lifeline networks. First, a complementary structural function is established and three theorems are presented as a premise of the proposed algorithm. Taking the minimal cut of a network as decomposition policy, the proposed algorithm constructs a recursive decomposition process. During the decomposition, both the disjoint minimal cut set and the disjoint minimal path set are simultaneously enumerated. Therefore, in addition to obtaining an accurate value after decomposing all disjoint minimal cuts and disjoint minimal paths, the algorithm provides approximate results which satisfy a prescribed error bound using a probabilistic inequality. Two example networks, including a large urban gas system, are analyzed using the proposed algorithm. Meanwhile, a part of the results are compared with the results obtained by a path-based recursive decomposition algorithm. These results show that the proposed algorithm provides a useful probabilistic analysis method for the reliability evaluation of lifeline networks and may be more suitable for networks where the edges have low reliabilities.

An improved recursive decomposition algorithm for reliability evaluation of lifeline networks

The seismic reliability evaluation of lifeline networks has received considerable attention and been widely studied. In this paper, on the basis of an original recursive decomposition algorithm, an improved analytical approach to evaluate the seismic reliability of large lifeline systems is presented. The proposed algorithm takes the shortest path from the source to the sink of a network as decomposition policy. Using the Boolean laws of set operation and the probabilistic operation principal, a recursive decomposition process is constructed in which the disjoint minimal path set and the disjoint minimal cut set are simultaneously enumerated. As the result, a probabilistic inequality can be used to provide results that satisfy a prescribed error bound. During the decomposition process, different from the original recursive decomposition algorithm which only removes edges to simplify the network, the proposed algorithm simplifies the network by merging nodes into sources and removing edges. As a result, the proposed algorithm can obtain simpler networks. Moreover, for a network owning s-independent components in its component set, two network reduction techniques are introduced to speed up the proposed algorithm. A series of case studies, including an actual water distribution network and a large urban gas system, are calculated using the proposed algorithm. The results indicate that the proposed algorithm provides a useful probabilistic analysis method for the seismic reliability evaluation of lifeline networks.

A Kind of Second-Order Learning Algorithm Based on Generalized Cost Criteria in Multi-Layer Feed-Forward Neural Networks

A kind of second order algorithm--recursive approximate Newton algorithm was given by Karayiannis. The algorithm was simplified when it was formulated. Especially, the simplification to matrix Hessian was very reluctant, which led to the loss of valuable information and affected performance of the algorithm to certain extent. For multi layer feed forward neural networks, the second order back propagation recursive algorithm based generalized cost criteria was proposed. It is proved that it is equivalent to Newton recursive algorithm and has a second order convergent rate. The performance and application prospect are analyzed. Lots of simulation experiments indicate that the calculation of the new algorithm is almost equivalent to the recursive least square multiple algorithm. The algorithm and selection of networks parameters are significant and the performance is more excellent than BP algorithm and the second order learning algorithm that was given by Karayiannis.

Prediction of Time Series Empowered with a Novel SREKRLS Algorithm

For the unforced dynamical non-linear state–space model,a new Q1 and efficient square root extended kernel recursive least square estimation algorithm is developed in this article.The proposed algorithm lends itself towards the parallel implementation as in the FPGA systems.With the help of an ortho-normal triangularization method,which relies on numerically stable givens rotation,matrix inversion causes a computational burden,is reduced.Matrix computation possesses many excellent numerical properties such as singularity,symmetry,skew symmetry,and triangularity is achieved by using this algorithm.The proposed method is validated for the prediction of stationary and non-stationary Mackey–Glass Time Series,along with that a component in the x-direction of the Lorenz Times Series is also predicted to illustrate its usefulness.By the learning curves regarding mean square error(MSE)are witnessed for demonstration with prediction performance of the proposed algorithm from where it’s concluded that the proposed algorithm performs better than EKRLS.This new SREKRLS based design positively offers an innovative era towards non-linear systolic arrays,which is efficient in developing very-large-scale integration(VLSI)applications with non-linear input data.Multiple experiments are carried out to validate the reliability,effectiveness,and applicability of the proposed algorithm and with different noise levels compared to the Extended kernel recursive least-squares(EKRLS)algorithm.

A Simple Hybrid Recursive Learning Algorithm with High Generalization Performance for Radial Basis Function Neural Network

In this paper, we propose a simple learning algorithm for non\|linear function approximation and system modeling using minimal radial basis function neural network with high generalization performance. A hybrid algorithm is constructed, which combines recursive n \|means clustering algorithm with a simple recursive regularized least squares algorithm (SRRLS). The n \|means clustering algorithm adjusts the centers of the network, while the SRRLS constructs a parsimonious network which makes the generalization performance of the network well. The SRRLS algorithm needs no matrix computing, so it has a lower computational cost and no ill\|conditional problem. Because of the recursive manner, this algorithm is suitable for on\|line applications. The effectiveness of this algorithm is demonstrated by two benchmark examples.

Generating routes for autonomous driving in vehicle-to-infrastructure communications

The study of vehicular networks has attracted considerable interest in academia and the industry.In the broad area,connected vehicles and autonomous driving are technologies based on wireless data communication between vehicles or between vehicles and infrastructures.A Vehicle-to-Infrastructure(V2I)system consists of communications and computing over vehicles and related infrastructures.In such a system,wireless sensors are installed in some selected points along roads or driving areas.In autonomous driving,it is crucial for a vehicle to figure out the ideal routes by the communications between its equipped sensors and infrastructures then the vehicle is automatically moving along the routes.In this paper,we propose a Bezier curve based recursive algorithm,which effectively creates routes for vehicles through the communication between the On-Board Unit(OBU)and the Road-Side Units(RSUs).In addition,this approach generates a very low overhead.We conduct simulations to test the proposed algorithm in various situations.The experiment results demonstrate that our algorithm creates almost ideal routes.

Unifying representation of Bézier curve and two kinds of generalized ball curves

This paper presents a new basis, the WSB basis, which unifies the Bemstein basis, Wang-Ball basis and Said-Ball basis, and therefore the Bézier curve, Wang-Ball curve and Said-Ball curve are the special cases of the WSB curve based on the WSB basis In addition, the relative degree elevation formula, recursive algorithm and conversion formula between the WSB basis and the Bern- stein basis are given.

Instability of Solution of Phase Retrieval in Direct Diffraction Phase-Contrast Imaging with Partially Coherent X-Ray Source

The theoretical model of direct diffraction phase-contrast imaging with partially coherent x-ray source is expressed by an operator of multiple integral. It is presented that the integral operator is linear. The problem of its phase retrieval is described by solving an operator equation of multiple integral. It is demonstrated that the solution of the phase retrieval is unstable. The numerical simulation is performed and the result validates that the solution of the phase retrieval is unstable.