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A robust algorithm for solving nonlinear system of equations using trust-region and line-search techniques 利用信赖域和线搜索技术求解非线性方程组的鲁棒算法
Int. J. Comput. Sci. Math. Pub Date : 2020-03-31 DOI: 10.1504/ijcsm.2020.10028095
M. Kabir
{"title":"A robust algorithm for solving nonlinear system of equations using trust-region and line-search techniques","authors":"M. Kabir","doi":"10.1504/ijcsm.2020.10028095","DOIUrl":"https://doi.org/10.1504/ijcsm.2020.10028095","url":null,"abstract":"Newton's method is an attractive method for solving nonlinear system of equations because of its fast convergence property. However, Newton's method may fail if the Jacobian matrices are singular. Newton's method with trust-region can be used to avoid such problem. In this work, a new trust-region technique for Newton's method was formulated to solve the nonlinear system of equations. The search direction in this method is computed by a sequence of factorisations of the Jacobian matrix with modified structure using a Lagrange multiplier associated with trust-region constraint such that the final modified Jacobian turns out to be well-conditioned (regularised). An optimal Lagrange multiplier was deduced using the same idea of unconstrained optimisation to satisfy the trust-region constraint. Furthermore, Armijo line-search technique is integrated with the method in order to improve the step length. Numerical tests were conducted to investigate the performance of Newton's method integrated with trust-region and line-search techniques.","PeriodicalId":399731,"journal":{"name":"Int. J. Comput. Sci. Math.","volume":"198 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2020-03-31","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"132301808","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
引用次数: 2
Quartic Padé approximation to the exponential function and a class of local analytical difference schemes 指数函数的四次逼近及一类局部解析差分格式
Int. J. Comput. Sci. Math. Pub Date : 2020-03-31 DOI: 10.1504/ijcsm.2020.10028093
C. Zheng, Yan Xiao
{"title":"Quartic Padé approximation to the exponential function and a class of local analytical difference schemes","authors":"C. Zheng, Yan Xiao","doi":"10.1504/ijcsm.2020.10028093","DOIUrl":"https://doi.org/10.1504/ijcsm.2020.10028093","url":null,"abstract":"This paper investigates the quartic non-diagonal algebraic Hermite-Pade approximation to the exponential function. Explicit formulas and differential equations are obtained for the polynomial coefficients. An exact asymptotic expression is obtained for the error function. As an application, a class of local analytical difference schemes based on quartic Pade approximation for diffusion-convection equation with constant coefficients are proposed. A numerical example is provided to demonstrate the effectiveness of the theoretical results.","PeriodicalId":399731,"journal":{"name":"Int. J. Comput. Sci. Math.","volume":"11 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2020-03-31","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"126639462","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
引用次数: 0
Multivariate generalised gamma kernel density estimators and application to non-negative data 多元广义核密度估计及其在非负数据上的应用
Int. J. Comput. Sci. Math. Pub Date : 2020-03-31 DOI: 10.1504/ijcsm.2020.10028092
L. Harfouche, N. Zougab, S. Adjabi
{"title":"Multivariate generalised gamma kernel density estimators and application to non-negative data","authors":"L. Harfouche, N. Zougab, S. Adjabi","doi":"10.1504/ijcsm.2020.10028092","DOIUrl":"https://doi.org/10.1504/ijcsm.2020.10028092","url":null,"abstract":"This paper proposes a classical multivariate generalised gamma (GG) kernel estimator for probability density function (pdf) estimation in the context of multivariate nonnegative data. Then, we show that the multiplicative bias correction (MBC) techniques can be applied for multivariate GG kernel density estimator as in Funke and Kawka (2015). Some properties (bias, variance and mean integrated squared error) of the corresponding estimators are also provided. The choice of the vector of bandwidths is investigated by adopting the popular cross-validation technique. Finally, the performances of the classical and MBC estimator based on the family of GG kernels are illustrated by a simulation study and real data.","PeriodicalId":399731,"journal":{"name":"Int. J. Comput. Sci. Math.","volume":"2 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2020-03-31","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"134164574","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
引用次数: 5
Optimisation of makespan of a flow shop problem using multi layer neural network 基于多层神经网络的流水车间最大完工时间优化
Int. J. Comput. Sci. Math. Pub Date : 2020-03-31 DOI: 10.1504/ijcsm.2020.10028046
H. Kumar, S. Giri
{"title":"Optimisation of makespan of a flow shop problem using multi layer neural network","authors":"H. Kumar, S. Giri","doi":"10.1504/ijcsm.2020.10028046","DOIUrl":"https://doi.org/10.1504/ijcsm.2020.10028046","url":null,"abstract":"This paper presents an approach based on a multi layer neural network algorithm (MLNNA) to find a sequence of jobs for flow shop scheduling problems with the objective of minimise the makespan. The purpose of this paper is to develop an artificial intelligence and trained a neural network model for solving the flow shop scheduling problem which gives a best jobs sequence with the objective of minimise the makespan. The effectiveness of the proposed MLNNA method is compared with many problems selected from different papers. A large number of problems are solved with the present MLNNA model and it is found suitable and workable in all the cases.","PeriodicalId":399731,"journal":{"name":"Int. J. Comput. Sci. Math.","volume":"499 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2020-03-31","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"116131228","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
引用次数: 3
An easy-to-use computer program for standardisation methods of population morbidity data 一个易于使用的计算机程序，用于人口发病率数据的标准化方法
Int. J. Comput. Sci. Math. Pub Date : 2020-02-27 DOI: 10.1504/ijcsm.2020.105451
Mei‐Sing Ong, W. N. Arifin, N. Yaacob, N. Naing
{"title":"An easy-to-use computer program for standardisation methods of population morbidity data","authors":"Mei‐Sing Ong, W. N. Arifin, N. Yaacob, N. Naing","doi":"10.1504/ijcsm.2020.105451","DOIUrl":"https://doi.org/10.1504/ijcsm.2020.105451","url":null,"abstract":"Standardisation is an essential procedure to eliminate the effect of confounding when comparisons between populations are carried out, where a standard population is used as a reference. There are two methods of standardisation, i.e., direct and indirect standardisation. Standardisation is commonly used in epidemiology studies especially when the morbidity or/and mortality rates of a disease are studied. A computer program (StdAn) which aims to simplify the process of standardisation of population morbidity data was developed with Microsoft Visual Studio 2010 Express software, using C++/CLI (C++ on common language infrastructure) as the programming language. StdAn program provides a graphically easy-to-use interface for the implementation of standardisation analysis. It is simple, practical and easy to interpret.","PeriodicalId":399731,"journal":{"name":"Int. J. Comput. Sci. Math.","volume":"11 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2020-02-27","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"116656196","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
引用次数: 0
Image reconstruction based on approximate function and modified conjugate gradient 基于近似函数和修正共轭梯度的图像重构
Int. J. Comput. Sci. Math. Pub Date : 2020-02-27 DOI: 10.1504/ijcsm.2020.105448
Ping Gong, Guohua Li, Jian Li
{"title":"Image reconstruction based on approximate function and modified conjugate gradient","authors":"Ping Gong, Guohua Li, Jian Li","doi":"10.1504/ijcsm.2020.105448","DOIUrl":"https://doi.org/10.1504/ijcsm.2020.105448","url":null,"abstract":"This paper proposed an approach combines the advantages of L1 norm and TV norm by combining L1 norm and TV norm to solve the image reconstruction problems. And the proposed approach reconstructs an image from the measured values by using the modified conjugate gradient algorithm for the purpose of improving the efficiency of image reconstruction. The objective function is constructed using the approximate function based on the L1 norm and TV norm. A sparse transformation is applied to the original image first. The random Gaussian matrix is then employed to perform a compressive measurement on the 2-D sparse signal. To reconstruct the image a regularised reconstruction model is established through the approximate norm that combines L1 norm and TV norm and the gradient of the approximate norm is computed. The simulation results demonstrate the ability of the proposed method to reconstruct images more effectively and produce better results in terms of objective indicators such as PSNR and SSIM than classical methods.","PeriodicalId":399731,"journal":{"name":"Int. J. Comput. Sci. Math.","volume":"11 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2020-02-27","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"128959903","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
引用次数: 0
A robust second order numerical method for a weakly coupled system of singularly perturbed reaction-diffusion problem with discontinuous source term 源项不连续的弱耦合奇摄动反应扩散问题的二阶鲁棒数值解法
Int. J. Comput. Sci. Math. Pub Date : 2020-02-27 DOI: 10.1504/ijcsm.2020.105449
P. M. Basha, V. Shanthi
{"title":"A robust second order numerical method for a weakly coupled system of singularly perturbed reaction-diffusion problem with discontinuous source term","authors":"P. M. Basha, V. Shanthi","doi":"10.1504/ijcsm.2020.105449","DOIUrl":"https://doi.org/10.1504/ijcsm.2020.105449","url":null,"abstract":"In this paper, a fitted mesh numerical method on Shishkin mesh is proposed to solve a weakly coupled system of two singularly perturbed reaction-diffusion equations containing equal diffusion parameters with discontinuous source terms. This method uses the standard centred finite difference scheme constructed on piecewise-uniform Shishkin mesh with the average of the source terms on either side of the point of discontinuity and then the problem is solved by an iterative procedure. An error analysis is carried out and the method ensures that the parameter-uniform convergence of almost the second order. Numerical results are provided to confirm the theoretical results and compares well with the existing results.","PeriodicalId":399731,"journal":{"name":"Int. J. Comput. Sci. Math.","volume":" 25","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2020-02-27","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"120834137","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
引用次数: 1
Research on Chinese well-known e-commerce enterprises' innovation ability based on real comment 基于真实评价的中国知名电子商务企业创新能力研究
Int. J. Comput. Sci. Math. Pub Date : 2020-02-27 DOI: 10.1504/ijcsm.2020.105459
Shufang Li, Changbing Jiang, Liang Li
{"title":"Research on Chinese well-known e-commerce enterprises' innovation ability based on real comment","authors":"Shufang Li, Changbing Jiang, Liang Li","doi":"10.1504/ijcsm.2020.105459","DOIUrl":"https://doi.org/10.1504/ijcsm.2020.105459","url":null,"abstract":"Based on the real comments from Jingdong Mall, T-mall and other e-commerce platforms as for the data resource, according to analysis to the customers' online shopping comments' vocabularies, obtained 11 indicators which are constituted e vocabularies, obtained 11 indicators which are constituted e-commerce platform customer satisfaction index system and the satisfaction indicator value, using projection pursuit model (PPM) and genetic algorithms to make a further calculation to satisfaction indicators. The results show that: which has the greatest impact on e-commerce platforms' overall satisfaction is the product reputation and popularity; Jingdong Mall has the best overall satisfaction among Jingdong Mall, T-mall, and Amazon this three e-commerce platforms. Meanwhile, each ecommerce platforms has its own superiority and own superiority and weakness.","PeriodicalId":399731,"journal":{"name":"Int. J. Comput. Sci. Math.","volume":"4 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2020-02-27","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"128142997","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
引用次数: 1
Stationary distribution and ergodicity of a stochastic single-species model under regime switching in a polluted environment 污染环境中状态切换下随机单物种模型的平稳分布和遍历性
Int. J. Comput. Sci. Math. Pub Date : 2020-02-27 DOI: 10.1504/ijcsm.2020.105450
Yu Zhao, C. Zhai
{"title":"Stationary distribution and ergodicity of a stochastic single-species model under regime switching in a polluted environment","authors":"Yu Zhao, C. Zhai","doi":"10.1504/ijcsm.2020.105450","DOIUrl":"https://doi.org/10.1504/ijcsm.2020.105450","url":null,"abstract":"The long-term statistical rule is one of the important questions for stochastic pollution-population dynamical models, thus it would be worth looking for the stationary distribution as an indicator in analysing the effects of toxicant and noises on the variation of population in evolution process. In present paper, we investigate a stochastic single-species model under regime switching in a polluted environment. By use of the ergodic of Markov chain and constructing Lyapunov function, the sufficient conditions for the positive recurrence and ergodic property are established, which imply the existence of stationary distribution of the model. Moreover, the mean and variance of marginal stationary distribution are estimated. Our analysis indicates that the coloured noise and toxicant may play an important role in determining the shape of stationary distribution and its statistics characteristics. Finally, numerical simulations are carried out to support our theoretical results.","PeriodicalId":399731,"journal":{"name":"Int. J. Comput. Sci. Math.","volume":"22 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2020-02-27","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"114680838","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
引用次数: 0
Local search-based dynamically adapted bat algorithm in image enhancement domain 图像增强领域基于局部搜索的动态自适应bat算法
Int. J. Comput. Sci. Math. Pub Date : 2020-02-27 DOI: 10.1504/ijcsm.2020.105447
K. G. Dhal, Sanjoy Das
{"title":"Local search-based dynamically adapted bat algorithm in image enhancement domain","authors":"K. G. Dhal, Sanjoy Das","doi":"10.1504/ijcsm.2020.105447","DOIUrl":"https://doi.org/10.1504/ijcsm.2020.105447","url":null,"abstract":"Bat algorithm (BA) is a new metaheuristic optimisation algorithm, which has already proved its supreme performance on many optimisation fields. However, it is possible to increase its efficiency when solving complex optimisation problems. This study concentrates on improving the efficiency of BA by incorporating different types of local search strategies and novel self-adaption strategies of parameters such as loudness, pulse rate and frequency. Comparative analysis of three different proposed local search strategies has been performed to find the best one. The proposed modified BAs with local search strategies are employed to solve five popular image enhancement models. Experimental results prove that self-adaption of parameters enhances the capability of standard BA. But the addition of efficient local search technique with self-adaption increases the effectiveness of the standard BA to a great extent.","PeriodicalId":399731,"journal":{"name":"Int. J. Comput. Sci. Math.","volume":"1 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2020-02-27","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"123727310","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
引用次数: 18
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