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.

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 Heuristic Recursive Strategy Based on Genetic Algorithm for the Strip Rectangular Packing Problem

与基因算法结合的改进启发式的递归的策略在这份报纸被介绍。第一，这个方法寻找一些矩形，它有一样的长度或宽度，到没有浪费空间，形成一些层，然后，计算留下包装顺序的高度使用启发式的递归的策略并且使用基因算法的进化能力减少高度。基准问题的几个班上的计算结果证明了介绍算法能与已知的进化启发规则竞争。它特别为大测试问题更好表现。

A New Recursive Parameter Estimation Algorithm of Multi－Variable Time－Varying AR Model

A new recursive algorithm of multi variable time varying AR model is proposed. By changing the form of AR model, the parameter estimation can be regarded as state estimation of state equations. Then the Kalman filter is used to estimate the variation of

NEW EFFICIENT ORDER-RECURSIVE LEAST-SQUARES ALGORITHMS

Order-recursive least-squares(ORLS)algorithms are applied to the prob-lems of estimation and identification of FIR or ARMA system parameters where a fixedset of input signal samples is available and the desired order of the underlying model isunknown.On the basis of several universal formulae for updating nonsymmetric projec-tion operators,this paper presents three kinds of LS algorithms,called nonsymmetric,symmetric and square root normalized fast ORLS algorithms,respectively.As to the au-thors’ knowledge,the first and the third have not been so far provided,and the second isone of those which have the lowest computational requirement.Several simplified versionsof the algorithms are also considered.

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.

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.

BLOCK ADAPTIVE RECURSIVE ALGORITHM FOR VIDEO CONFERENCE CODING

This paper presents a new motion estimation algorithm for video conference signal coding. This type of algorithm is called block adaptive recursive algorithm (BARA). Simulation results show that this new algorithm has better performance than conventional ones.

RECURSIVE ALGORITHM FOR ADAPTIVE ARRAYS AND SYSTOLIC ARRAY IMPLEMENTATION

In this paper, a new recursive algorithm of adaptive array weight vectors and its systolic array implementing structure is proposed, which is based on the QR decomposition algorithms and the idea of algorithmic engineering. The algorithm can realize fully parallel and pipeline processing.

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.

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 Alternate Operation Strategy in Sequential Tests

Based on the sequential probability ratio test(SPRT)developed by Wald,an improved method for successful probability test of missile flight is proposed.A recursive algorithm and its program in Matlab are designed to calculate the real risk level of the sequential test decision and the average number of samples under various test conditions.A concept,that is "rejecting as soon as possible",is put forward and an alternate operation strategy is conducted.The simulation results show that it can reduce the test expenses.

The Application Research of a Fast Recursive Predictive Algorithm on Medical X-ray Image Compression

This paper studied a fast recursive predictive algorithm used for medical X-ray image compression. This algorithm consists of mathematics model building, fast recursive algorithm deducing, initial value determining, step-size selecting, image compression encoding and original image recovering. The experiment result indicates that this algorithm has not only a higher compression ratio to medical X-ray images compression, but also promotes image compression speed greatly.

递归型数据中心网络上g-额外连通度及容错单播算法研究

数据中心网络的研究是近几年兴起的热点。与传统的树型数据中心网络相比,递归型数据中心网络具有更好的容错性和可扩展性。部署于n-口交换机上的k-维递归型完全图网络可以表示为Xk,n,σ表示图中任意顶点与同维度其他子图相连接的边数。在实际情况中,网络的额外连通度相较于传统的连通度能够更准确地衡量一个网络的容错性。证明当k≥3,n≥3,σ∈{1,n-1}且0≤g≤2时,Xk,n的g-额外连通度为(g+1)(kσ-1)+n,这一结果接近于其连通度的g+1倍。进一步,提出基于该情形下的容错单播算法,并证明了该算法的时间复杂度和在最坏情况下Xk,n中任意两点间构造出路径长度的上界。通过模拟仿真实验,验证了该算法在执行效率上优于广度优先和深度优先搜索算法,且算法具有较好的容错性。

基于不同算法筛选糖尿病足溃疡截肢预测模型的比较

目的 探讨不同算法筛选的糖尿病足溃疡(DFU)截肢预测模型。方法 收集2015年1月至2020年12月新疆医科大学第一附属医院收治的364例DFU患者的临床资料,按照截肢情况将其分为截肢组(n=213)和非截肢组(n=151),分别通过单因素分析、Boruta算法和随机森林-递归特征消除(RF-RFE)算法进行截肢危险因素分析,并构建临床预测模型,比较模型的c指数、F1分数和Brier分数,评估模型的预测效能和临床意义。结果 两组患者年龄、高血压病程、冠心病病程、Wagner评分、部位-缺血-神经病变-细菌感染-面积-深度(SINBAD)评分、国际糖尿病足工作组(IWGDF)分级比较,差异均有统计学意义(P﹤0.05)。实验室指标中截肢组患者低密度脂蛋白(LDL)、高密度脂蛋白(HDL)、甘油三酯(TG)、血钙、血磷、白蛋白与球蛋白比值(A/G)、平均血小板分布宽度(PDW)、血红蛋白(Hb)均低于非截肢组患者,截肢组患者球蛋白(GB)、中性粒细胞比例(N)、纤维蛋白原(FIB)、国际标准化比值(INR)、平均红细胞分布宽度(RDW)/白蛋白比率、中性粒细胞/淋巴细胞比值(NLR)、血小板与淋巴细胞比值(PLR)均高于非截肢组患者,差异均有统计学意义(P﹤0.05)。多因素分析结果显示,Wagner分级﹥2级、SINBAD评分﹥3分、FIB、Hb、PDW、INR、年龄均是DFU患者截肢的独立危险因素(P﹤0.05)。传统Logistic回归模型c指数、F1分数和Brier分数分别为0.771、0.809、0.163。采用Boruta算法得出对截肢影响最大的影响因素为年龄、Wagner分级﹥2级、SINBAD评分﹥3分、IWGDF分级﹥3级、A/G、INR、FIB、N、Hb、RDW比白蛋白比率、NLR和PLR,模型c指数、F1分数、Brier分数分别为0.686、0.744、0.163.RF-RFE算法得出DFU截肢危险因素为NLR、PLR、N、肌酐和PDW,模型c指数、F1分数和Brier分数分别为0.748、0.769、0.220。结论 不同算法从不同逻辑对DFU患者截肢的危险因素进行评估,可与传统统计学方法结合,为DFU的治疗决策提供依据互补。