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Mathematical Theory and Applications 2016 Vol.36 Please wait a minute... For Selected: Download Citations EndNote Ris BibTeX Toggle Thumbnails Select An Inexact Broyden Method for Nonlinear Equations Wu Peiyu, Zhang Li Mathematical Theory and Applications    2016, 36 (2): 1-9.   Abstract （661）      PDF（pc） （447KB）（39）       Knowledge map    This paper introduces an inexact Broyden method for solving nonlinear equations,which is an extension of the method in[8].Under appropriate conditions,we prove that the proposed method converges globally and superlinearly.Numerical results are given to show its efficiency. Related Articles | Metrics Select Constructing a Symmetric Tridiagonal Matrix Based on Its Defective Generalized Eigenpair and Nonleading Principle Submatrix Zhu Qundi, Hong Pingzhou, Huang Xiantong Mathematical Theory and Applications    2016, 36 (2): 10-21.   Abstract （705）      PDF（pc） （429KB）（37）       Knowledge map    In this paper we consider the equation AnX =λCnX ,where Anis a symmetric tridiagonal matrix and Cnis a diagonal matrix.Regarding Anas a 3×3blocked matrix,given a(r+1)×(r+s)non-sequential principle submatrix of An ,given Cn ,four vectors X1 = (x1,…,xr)＇,X3=(xr+s+1,…,xn)＇,Y1 = (y1,…,yr)＇,Y3=(yr+s+1,…,yn)＇and two distinct real numbersλ,μ,we construct a symmetric tridiagonal matrix Anand two vectors X2 = (xr+1,…,xr+s)＇,Y2= (yr+1,…,yr+s)＇such that AnX =λCn X and AnY =μCn Y ,where X = (X1＇, X2＇,X3＇)＇,Y = (Y1＇,Y2＇,Y3＇)＇.The existence conditions such that the problem has a solution and the corresponding algorithm to find the solutions are given.A numerical example is presented to show the validity of the algorithm. Related Articles | Metrics Select The Maximum Value for the Harary Index of Unicyclic Graphs with a Given Girth Chen Dandan Mathematical Theory and Applications    2016, 36 (2): 22-27.   Abstract （560）      PDF（pc） （234KB）（32）       Knowledge map    In this paper,we first give a formula for calculating the Harary index of a unicyclic graph according to the structure,and then using this formula,we obtain the maximum value for the Harary index of unicyclic graphs with a given girth,and characterize the extremal graph with respect to the Harary index. Related Articles | Metrics Select Moment Exponential Stability Analysis for a Class of Impulsive Stochastic Neural Networks Liu Xinge, Wang Fengxian, Tang Meilan Mathematical Theory and Applications    2016, 36 (3): 1-4.   Abstract （1284）      PDF（pc） （181KB）（332）       Knowledge map    Based on the mathematical induction,a novel sufficient condition on exponential stability in mean square and a new moment exponential stability condition are proposed for a class of impulsive stochastic neural networks,which are with less conservatism. Related Articles | Metrics Select Relations Between Several Ideals of a Ring and Its Quotient Ring Guan Zhengxiong, Wang Yao Mathematical Theory and Applications    2016, 36 (3): 5-11.   Abstract （1252）      PDF（pc） （268KB）（167）       Knowledge map    In this note,we investigate the relationships between ideals of a ring Rand its quotient ring R/I.We show that if I ⊆K ⊆ Rand I△R,then Kis a 2-primal ideal(strongly prime ideal,left T-nilpotent ideal, radically-symmetric ideal)of Rif and only if K/Iis a 2-primal ideal(strongly prime ideal,left T-nilpotent ideal,radically-symmetric ideal)of R/I. Related Articles | Metrics Select Lower Bounds of the Life Span of Classical Solutions to a System of Nonlinear Wave Equations with Weighted Function in Two Space Dimensions Wang Husheng, Sun Haixia, Mi Cailian Mathematical Theory and Applications    2016, 36 (3): 12-24.   Abstract （1304）      PDF（pc） （462KB）（166）       Knowledge map    This paper concerns the Cauchy problem of a nonlinear wave equation system with weighted function.Lower bounds to the life span of classical solutions with small initial values are derived,which generalizes the known results. Related Articles | Metrics Select Noise Supress Exponential Growth for Cohen-Grossberg Neural Networks Juanjun Wang, Qiao Lin, Hui Su Mathematical Theory and Applications    2016, 36 (3): 25-36.   Abstract （1231）      PDF（pc） （437KB）（221）       Knowledge map    In this letter,we will show that noise can make a given Cohen-Grossberg neural networks whose solution may grows exponentially become the new stochastic Cohen-Grossberg neural networks whose solution will grow at most polynomially.In other words,we reveal that the noise can suppress the exponential growth for Cohen-Grossberg neural networks. Related Articles | Metrics Select An Existence Theorem on Elliptic Partial Differential Equation with Square Integrable Leading Coefficients Li Yang Mathematical Theory and Applications    2016, 36 (3): 37-41.   Abstract （1233）      PDF（pc） （215KB）（204）       Knowledge map    In this paper we give the existence of weak solutions to a second order elliptic partial differential equation with square integrable regularity of leading coefficients.Specifically,we consider the elliptic equation - ∂ j(aij(x) ∂iu)=f0 + ∂ifi inΩ,u =0on the boundary,with aij =aji，aij uniform elliptic,and aij ∈L2(Ω).First,we approximate aijby a(m)ij which belongs to L∞(Ω),and then prove the existence theorem by applying the well known results concerning solvability of elliptic partial differential equation together with the standard energy method. Related Articles | Metrics Select Characteristic Analysis and Detection of Abnormal Data in High Frequency Monitoring Data Li Ting, Kong Wenjia, Zhou Juan, Zheng Zhoushun Mathematical Theory and Applications    2016, 36 (3): 42-53.   Abstract （1394）      PDF（pc） （1227KB）（411）       Knowledge map    In this paper,by analyzing 60000high-frequency monitoring data of 10equipments in a thermal power plants,we find that abnormal data has two characteristics:outlier or abnormal segment.A denoising method based on the first-order forward difference and the frequency distribution to detect the outlier and abnormal data in the high-frequency is proposed.In this method the threshold of abnormal data is determined by the risk probability and the frequency distribution of absolute value of the first-order forward difference, and the maximum number of the outliers included in the abnormal segment is obtained according to the performance of the device and the sampling frequency. The judgment rule for detecting abnormal data is then given with the threshold and the maximum number of the outliers.The method is applied to 6000data of a thermal power plant pre-pump motor for showing its effectiveness. Related Articles | Metrics Select Option Pricing to a Continuous Dividend Payment Model Driven by an Asymmetric Jump-diffusion Liu Dongyan, Fan Sujun, Wang Bing Mathematical Theory and Applications    2016, 36 (3): 48-53.   Abstract （1326）      PDF（pc） （238KB）（159）       Knowledge map    Assuming that the stock company pays dividend continuously and the pricing process is an asymmetric jump-diffusion process,this paper establishes an European call option pricing model and solves it with the insurance actuary pricing method. Related Articles | Metrics Select A Compound Markov Binomial Model with Random Dividends and Stochastic Premium Income Fang Shizu, Qin Lihua Mathematical Theory and Applications    2016, 36 (3): 54-65.   Abstract （1316）      PDF（pc） （420KB）（225）       Knowledge map    Consider a compound Markov binomial model with random dividends and stochastic premium Income. The recursive formulas for the expected discounted penalty function are derived,and the existence and uniqueness of the solutions to the recursive equations are proved.As applications,some examples concerning the quantities related to ruin are presented. Related Articles | Metrics Select Forecasting Stock Risks Based on a Physical Bubble Breakage Model Tian Zhikun Mathematical Theory and Applications    2016, 36 (3): 66-76.   Abstract （1303）      PDF（pc） （1394KB）（191）       Knowledge map     Since stock market bubbles are payed close attention by investors,it is meaningful to figure out the breakage time of the stock market bubble for investors to manage risks.In this paper by regarding the stock market bubbles as physical bubbles and taking into account the fluctuations of stock market,a model to depict the stock market bubbles is build.Parameters in the model are estimated by the least square method and genetic algorithm.Empirical analysis with our model on the Shanghai securities composite indexes of three time intervals shows that the errors between the predicted breakage time and the real breakage time of stock market bubbles are small,and furthermore,the time of the bubble breakage forecasted is more likely after the real breakage time.The model is used to forecast the Shanghai securities composite indexes from January,2014 to June,2015,and it is found that the predicted breakage time is almost the same to the real breakage time, which demonstrates that our bubble model has good effects in depicting the risks in stock market. Related Articles | Metrics Select Optimal Portfolio Selection Problem with Liability and Return Rate Modulated by Markov Chain under Partial Information Zhou Yue Mathematical Theory and Applications    2016, 36 (3): 77-82.   Abstract （1236）      PDF（pc） （242KB）（267）       Knowledge map    It is well-known that a financial model with deterministic coefficients are only good for a relative short period of time and cannot respond to changing conditions.The information available to the investor is the filtration generated by the asset price processes only.The investor can in general not directly observe the mean return rate processes and the volatility process of the asset price process.A simplified continuous time financial market with one risk-free asset(bond)and one risk asset(stock)were assumed.When the liability process is modeled by a linear-diffusion model and the mean return rates is modulated by a finite state continuous-time Markov chain,we estimate the mean return rates of stock under the Woham filter.By using the stochastic linear-quadratic control technique,the closed form solutions of the optimal portfolio strategy and the maximal expected exponential utility are obtained under the partial information. Related Articles | Metrics Select Research and Application of Multiple Attribute Decision Making Method with Interval Fuzzy Numbers Zhou Yicheng, Yao Jian Mathematical Theory and Applications    2016, 36 (3): 83-92.   Abstract （1293）      PDF（pc） （965KB）（451）       Knowledge map    In this paper some approaches are used to improve the multiple attribute decision making method. Firstly,direct and feasible interval hesitate fuzzy numbers are converted into intuitionistic fuzzy numbers,and overlapping intervals are employed to reduce numbers of attribute value elements,then the weights of attributes are determined by optimization,and finally,the mechanism of interval hesitate numbers and the applicability of real problems are taking into account to give evaluation on a regional enterprise. Related Articles | Metrics Select Research on the Fuzzy Membership Function Determination Based on Probability Statistics Ma Wanyuan, Geng Xiuli Mathematical Theory and Applications    2016, 36 (3): 93-100.   Abstract （1219）      PDF（pc） （682KB）（706）       Knowledge map    The key of using fuzzy mathematics to solve practical problems is to establish realistic membership function.The commonly used method to compute the fuzzy membership function is fuzzy statistic method, which relies on a large number of survey data and analysis on the function graph,and the calculation with heavy workload and complex process limits the practical application of fuzzy technology.A method for determining the fuzzy membership function based on probability statistics is proposed from the view of statistics.The proposed method is relatively simple and can adapt to much more cases of fuzzy membership function determination. Finally,a real world case is given and membership function curves derived from two methods are compared to verify the proposed method having higher accuracy. Related Articles | Metrics Select Comprehensive Risk Evaluation of Haze for Economic and Social Development in Yangtze River Delta District Jiang Mianfeng, Ye Chunming Mathematical Theory and Applications    2016, 36 (3): 101-111.   Abstract （1151）      PDF（pc） （694KB）（216）       Knowledge map    The aim of the paper is to make a comprehensive risk evaluation of potential hazard from Haze weather.We constructed the evaluation system of indicating factors which consists of 21indicators in 3categories on the basis of disaster systemic theory.We combined the Analytical Hierarchy Process(AHP)and the entropy approach to determine these indicators’weight.With the indicator system and its weights in hand,we calculate the correlation coefficient of comprehensive risk of haze pollution of three provinces in in Yangtze River delta district.The results indicated that the security risk level of Shanghai Jiangsu and Zhejiang isⅣ,Ⅱand Ⅰrespectively.The evaluation result based on matter-element extension model was accord with the result of traditional comprehensive index evaluation method,which proved that this model was reliable.In addition,we classified evaluation index in terms of weight,security level and improve difficulty,and find key index to reduce the risk level quickly. Related Articles | Metrics Select Empirical Analysis on the Relationship Between Housing Price Volatility and Main Economic Factors:Based on an ECM Model Zhang Hui, Rao Haiqin Mathematical Theory and Applications    2016, 36 (3): 112-118.   Abstract （1296）      PDF（pc） （2228KB）（262）       Knowledge map    The most cost of real estate prices is produced in the process of the development and construction of the house,but housing price volatility is influenced by many factors.In recent years,with the growing amount of total GDP and the per capita disposable income,the rapid expansion of urban population,China’s real estate market has developed rapidly,the housing price is up all the way.This paper investigates the relationship between housing price and various economic factors.Based on the annual data 2000-2014average price of China＇s real estate and the main economic factors GDP,the urban residents living disposable income,more than 5 years lending rate,money supply M1and the exchange rate against the U.S.dollar,this paper establishes a vector autoregression(VAR)model and modifies through a variety of statistical analysis.According to the modified ECM model,we get a conclusion:the housing price can economically function back to ROE in the long term. The short-term America subprime crisis could make the housing price play apositive influence on the ROE. Related Articles | Metrics Select An Automated Assessment Algorithm for Subjective Tests Zhu Shihua, Chen Ming Mathematical Theory and Applications    2016, 36 (3): 119-122.   Abstract （1364）      PDF（pc） （175KB）（282）       Knowledge map    In this paper,by improving the Single Similar Degree algorithm,a weighted Single Similar Degree algorithm is developed for automated assessment of subjective tests in the online exam system,which mainly considers the importance of the key words in the reference answer and gives each of the key words a certain weight.The improved algorithm has more accuracy for the assessment. Related Articles | Metrics Select The Exploration of Quality Assurance System for the Teaching of Mathematics and Statistics under the Construction of World-class(first-rate)Disciplines and Universities:Based on the Practice at Sun Yat-sen University Cheng Yuehua Mathematical Theory and Applications    2016, 36 (3): 123-128.   Abstract （1183）      PDF（pc） （222KB）（212）       Knowledge map     Under the new currency of constructing world-class disciplines and universities in the country, mathematics and statistics,as the undergraduate public basic courses of many disciplines and majors in the higher education,have had new tasks and become more important.In order to establish a better foundation for the relevant disciplines,as well as to achieve the goal of constructing world-class disciplines and universities, strengthening the quality assurance system of the public teaching for mathematics and statistics is crucial.This is also in regard to the potential tendency of the fusion of different disciplines,and the real needs from the development of those disciplines. Related Articles | Metrics Select The New Criteria of Generalized Nekrasov Matrices Su Anbing, Liu Jianzhou, Ding Biwen Mathematical Theory and Applications    2016, 36 (4): 1-7.   Abstract （1220）      PDF（pc） （265KB）（239）       Knowledge map    Generalized Nekrasov matrices have wide applications in economic mathematics,control theory and numerical algebra.In this paper,we consider the criteria of generalized Nekrasov matrices.Firstly,by applying inequality techniques and constructing positive diagonal matrix factors,we obtain several new criteria of generalized Nekrasov matrices based on the matrix elements, which extend some of the recent results.Then we give corresponding numerical examples to illustrate the effectiveness of the derived results. Related Articles | Metrics Select Flag-transitive Non-symmetric 2-designs with at Most 20 Points Liu Yan, Zhou Shenglin Mathematical Theory and Applications    2016, 36 (4): 8-17.   Abstract （1235）      PDF（pc） （356KB）（143）       Knowledge map    In this paper,we study the classification of flag-transitive nonsymmetric 2-(v,k,λ)designs with v ≤20.We prove that if(r,λ)=1then there are exactly 18non-isomorphic designs. Related Articles | Metrics Select BZ Derivations to the Lie Algebra of 4×4 Antisymmetric Matrices Over a Commutative Ring Liu Weili, Zhang Meili, Lu Huimin, Xie Jun Mathematical Theory and Applications    2016, 36 (4): 18-22.   Abstract （1434）      PDF（pc） （202KB）（368）       Knowledge map    Let Rbe a 2-torsion free commutative ring with identity.In this paper the decomposition of an arbitrary BZ derivation to the Lie algebra L4(R)of all 4×4antisymmetric matrices over Rand a sufficient and necessary condition for a BZ derivation to be an inner derivation are given. Related Articles | Metrics Select A Conjugate Gradient Iterative Algorithm for Hermitian Solutions of Matrix Equations with Constraints Yue Xiaorong, Zhou Fuzhao Mathematical Theory and Applications    2016, 36 (4): 23-28.   Abstract （1240）      PDF（pc） （234KB）（120）       Knowledge map    In this paper,we give a conjugate gradient iterative algorithm for Hermitian solutions of matrix equations under submatrix constraints.First,we transform the equations into two lower-order equations,then we construct a gradient iterative algorithm by conjugate gradients for lower-order equations to obtain the solutions and the optimal approximation of the matrix equations.Finally some numerical examples are given to verify the effectiveness of this method. Related Articles | Metrics Select An Inexact Regularized Newton Method for Monotone and Nonlinear Equations and its Local Convergence Li Weifei Mathematical Theory and Applications    2016, 36 (4): 29-35.   Abstract （1264）      PDF（pc） （566KB）（218）       Knowledge map    This paper presents an inexact regularized Newton method for monotone and nonlinear equations. Under relatively weak local error bound conditions,we show that the proposed method converges quadratically.This method is a generalization of the exact regularized Newton method proposed by Fan and Yuan[4]. Related Articles | Metrics Select Non-adjacent Vertices Neighborhood Union Condition for Fractional(g,f,m)-deleted Graphs Zhong Jiemei , Gao Wei Mathematical Theory and Applications    2016, 36 (4): 36-43.   Abstract （1235）      PDF（pc） （299KB）（152）       Knowledge map     A graph G is called a fractional(g,f,m)-deleted graph if the resulting graph admits a fractional(g,f)-factor after any medges are deleted.In this paper,we prove that if Gis a graph of order n,1≤a ≤g(x)≤f(x)-Δ≤b-Δ for any x∈V(G),δ(G)≥(b-Δ)(b+1)/a+2m,n≥(a+b)(2(a+b)+2m-1)/(a+Δ), and|NG(x1)∪NG(x2)|≥(b-Δ)n/(a+b) for any non-adjacent vertices x1 and x2,then G is a fractional(g,f,m)-deleted graph.The result is tight on the neighborhood union condition in some sense Related Articles | Metrics Select A Logarithmic Criterion for L1 -convergence of a Bisexual Branching Process in a Random Environment Zhou Yuanzheng, Wang Yuejiao, Qiu Yumei Mathematical Theory and Applications    2016, 36 (4): 44-49.   Abstract （1253）      PDF（pc） （251KB）（323）       Knowledge map    In this paper,the L1-convergence of a bisexual branching process in a random environment normalized by the upper bound of the conditional mean growth rate is investigated.A necessary and sufficient condition for theL1-convergence of the logarithmic criterion is given. Related Articles | Metrics Select Several Properties of the OROD Method for Solving the Sylvester Equation AXB+CX=D Deng Jianping Mathematical Theory and Applications    2016, 36 (4): 50-56.   Abstract （1234）      PDF（pc） （536KB）（208）       Knowledge map    This paper presents several properties of the OROD iterative method(orthogonal residual method and the orthogonal direction method)for solving the Sylvester equation AXB+CX= D.It is showed that the corresponding error sequence decreases monotonely.The minimization property of the method is precisely characterized.A numerical example is presented in the end. Related Articles | Metrics Select Initial Boundary Value Problem to a Generalized Kawahara Equation on a Bounded Interval or a Half-line Lu Meihong, Mi Cailian, Yang Han Mathematical Theory and Applications    2016, 36 (4): 57-71.   Abstract （1342）      PDF（pc） （552KB）（208）       Knowledge map    In this paper,we study the initial-boundary value problem to a generalized Kawahara equation on a bounded interval or a half-line.The energy integral method,the inequality technique and the embedding theorem are used to establish a prior estimate of the solution,and the existence and uniqueness of the global regular solution on a bounded interval are showed by the principle of contraction mapping.It is proved that the L2-norm of the solution has exponential decay when the time tends to infinity. Furthermore,under a stronger condition on the initial boundary values,the existence of a global regular solution on a bounded interval which is independent of the length of the bounded domain,and the existence of a unique global regular solution on a half -line are derived. Related Articles | Metrics Select The Survey and Analysis on the Aged People’s Life Quality in Changsha City First Social Welfare House Su Hui, Zhu Enwen, Qing Qingping Mathematical Theory and Applications    2016, 36 (4): 72-80.   Abstract （1264）      PDF（pc） （297KB）（97）       Knowledge map    In this paper,we investigate the aged people’s life quality by aquestionnaire survey on 100aged people lived in Changsha city first social welfare house.The classifications of K-means clustering upon the indexes of physiology,psychology,social relations and environments,and upon the self-assessment scores of life quality,respectively,show that the life quality of those aged people is slightly higher than the basic level. The single factor variance analysis indicates that the life quality is of statistical significance at difference of genders, marital status and pensions,but of non-statistical significance at difference of ages and education.And the correlation analysis demonstrates that the life quality of the aged people is positively correlated to the indexes of physiology, psychology,social relations and environments.It is found by stepwise regression that the main factors affecting the life quality of the aged people are the pension,the social relations,and the environment. The results of this study suggest that we should develop targeted measures based on the current situation and affecting factors to improve the life quality of the aged people in the welfare house. Related Articles | Metrics Select Investigation and Analysis on WeChat Payments Among College Students in Changsha City Chen Jing, Gu Xiaoxiao, Zhu Enwen Mathematical Theory and Applications    2016, 36 (4): 81-91.   Abstract （1306）      PDF（pc） （2110KB）（276）       Knowledge map    With the rise of e-commerce in the internet era,the online shopping has become a new consumer trend.With the rapid development of WeChat in the past few years,WeChat payments have greatly changed the pattern of Alipay or other third-party payment  platform monopoly market.In nowdays,college students as one of the main groups of WeChat payment and third-party payment will affect the future of WeChat＇s development to a large extent.A sampling survey via distributing questionnaire to college students in Changsha city is carried.Sample data are analyzed with the statistical software SPSS and Excel,and some suggestions are given based on the results from the data. Related Articles | Metrics Select Sample Learning Based on λ -increasing Function Li Jingjing, Tian Dagang Mathematical Theory and Applications    2016, 36 (4): 92-105.   Abstract （1221）      PDF（pc） （451KB）（251）       Knowledge map    How to determine the structure of a neural network is often an aporia in theoretical research and practical application.Based on the recent research of Vugar E.Ismailov,this paper study the learning method of sample points in neural network.The results show that with theλ -strictly increasing function,any specified sample set can be learnt by using only two neurons in hidden layer.The differences between using the usual Sigmoid function andλ -strictly increasing function as active function in the hidden layer are presented as well. Related Articles | Metrics Select Application of Copula Function in Financial Market Dong Zhiqian, Li Xingye Mathematical Theory and Applications    2016, 36 (4): 106-115.   Abstract （1303）      PDF（pc） （4470KB）（358）       Knowledge map    The paper studies the correlation between the stock market and the real estate stock(Vanke)and the tail dependence by establishing a copula model.Marginal distributions of the stock market and the real estate stock are estimated by the non-parametric kernel density estimation method.An optimal copula model is constructed by making use of the bivariate distribution histogram,quantile-quantile(Q-Q)plot,square Euclidean distance.Parameters in the model are estimated by the maximum likelihood estimation(MLE)method.Q-Q plot is applied on the test data without distribution function.The results show that the Binary t-copula model can fit the joint distribution of market and Vanke better than other models,the market and Vanke stock have a strong positive correlation,and the tail dependence under extreme cases is lower than the positive correlation under general cases. Related Articles | Metrics Select Application of GM (1,1)Model Based on Least Square Method in Vegetable Yield Forecast in China Wang Jie, Wang Bo Mathematical Theory and Applications    2016, 36 (4): 116-124.   Abstract （1247）      PDF（pc） （660KB）（164）       Knowledge map    Since 2011the production and output of vegetable in China have exceeded that of grain and become the largest agricultural product so that its production affects the stability of the national market.Owing to the production of vegetable being affected by many factors,the available data of the production have three shortages: large volatility,small sample size and poor information. In order to predict the vegetable yield in China in a short term,we apply a GM(1,1)model based on least square method and the gray system prediction theory, where the least square method is used to weaken the large fluctuation of data and to reduce the randomness. The predicting model is established with the vegetable production data of 2009to 2014and is showed with the data of 2014to have good forecasting accuracy.The forecasting results show that the production of vegetable will continue to increase in the next three years,which can provide some references for other related prediction, for facilitating the macro-regulation to the future vegetable market to maintain market balance and avoid risks of price fluctuation. Related Articles | Metrics Select Parallel Algorithm to the Inverse of Cyclic Toeplitz Matrices Xu Wenhua Mathematical Theory and Applications    2016, 36 (4): 125-128.   Abstract （1209）      PDF（pc） （166KB）（319）       Knowledge map    Toeplitz Matrices and theirs related equations have a wide application in mathematics,engineering and scientific calculation.This paper introduces the parallel algorithm to the inverse of cyclic Toeplitz Matrices. Related Articles | Metrics