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On the convergence of secant-like algorithms with applications to generalized fractional calculus 类sec算法的收敛性及其在广义分数阶微积分中的应用
Applicationes Mathematicae Pub Date : 2016-01-01 DOI: 10.4064/AM2275-12-2015
G. Anastassiou, I. Argyros
{"title":"On the convergence of secant-like algorithms with applications to generalized fractional calculus","authors":"G. Anastassiou, I. Argyros","doi":"10.4064/AM2275-12-2015","DOIUrl":"https://doi.org/10.4064/AM2275-12-2015","url":null,"abstract":"We present local and semilocal convergence results for secantlike algorithms in order to approximate a locally unique solution of a nonlinear equation in a Banach space setting. In the last part of the study we present some choices of the operators involved in fractional calculus where the operators satisfy the convergence conditions.","PeriodicalId":52313,"journal":{"name":"Applicationes Mathematicae","volume":"30 1","pages":"191-206"},"PeriodicalIF":0.0,"publicationDate":"2016-01-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"81487449","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
Local convergence for a family of iterative methods based on decomposition techniques 一类基于分解技术的迭代方法的局部收敛性
Applicationes Mathematicae Pub Date : 2016-01-01 DOI: 10.4064/AM2261-12-2015
I. Argyros, S. George, S. Erappa
{"title":"Local convergence for a family of iterative methods based on decomposition techniques","authors":"I. Argyros, S. George, S. Erappa","doi":"10.4064/AM2261-12-2015","DOIUrl":"https://doi.org/10.4064/AM2261-12-2015","url":null,"abstract":"We present a local convergence analysis for a family of iterative methods obtained by using decomposition techniques. The convergence of these methods was shown before using hypotheses on up to the seventh derivative although only the first derivative appears in these methods. In the present study we expand the applicability of these methods by showing convergence using only the first derivative. Moreover we present a radius of convergence and computable error bounds based only on Lipschitz constants. Numerical examples are also provided.","PeriodicalId":52313,"journal":{"name":"Applicationes Mathematicae","volume":"332 1","pages":"133-143"},"PeriodicalIF":0.0,"publicationDate":"2016-01-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"80552527","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
Functional central limit theorems for seeds in a linear birth and growth model 线性出生生长模型中种子的泛函中心极限定理
Applicationes Mathematicae Pub Date : 2016-01-01 DOI: 10.4064/AM2283-2-2016
A. Dziwisz, W. Szczotka
{"title":"Functional central limit theorems for seeds in a linear birth and growth model","authors":"A. Dziwisz, W. Szczotka","doi":"10.4064/AM2283-2-2016","DOIUrl":"https://doi.org/10.4064/AM2283-2-2016","url":null,"abstract":". A problem of heredity of mixing properties ( α -mixing, β -mixing and ρ -mixing) from a stationary point process on R × R + to a sequence of some of its points called ‘seeds’ is considered. Next, using the mixing properties, several versions of functional central limit theorems for the distances between seeds and the process of the number of seeds are obtained.","PeriodicalId":52313,"journal":{"name":"Applicationes Mathematicae","volume":"43 1","pages":"1-24"},"PeriodicalIF":0.0,"publicationDate":"2016-01-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"82006702","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
On the continuation of the limit distribution of central order statistics under power normalization 幂归一化下中心阶统计量极限分布的延拓
Applicationes Mathematicae Pub Date : 2016-01-01 DOI: 10.4064/am2247-2-2016
H. M. Barakat, E. Nigm, E. O. A. Zaid
{"title":"On the continuation of the limit distribution of central order statistics under power normalization","authors":"H. M. Barakat, E. Nigm, E. O. A. Zaid","doi":"10.4064/am2247-2-2016","DOIUrl":"https://doi.org/10.4064/am2247-2-2016","url":null,"abstract":"An important stability property of central order statistics under power normalization is discussed. It is proved that the restricted convergence of power normalized central order statistics on an arbitrary nondegenerate interval implies their weak convergence.","PeriodicalId":52313,"journal":{"name":"Applicationes Mathematicae","volume":"10 1","pages":"145-155"},"PeriodicalIF":0.0,"publicationDate":"2016-01-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"87423121","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
Conditional differential equations 条件微分方程
Applicationes Mathematicae Pub Date : 2016-01-01 DOI: 10.4064/AM2269-2-2016
C. Rom
{"title":"Conditional differential equations","authors":"C. Rom","doi":"10.4064/AM2269-2-2016","DOIUrl":"https://doi.org/10.4064/AM2269-2-2016","url":null,"abstract":"","PeriodicalId":52313,"journal":{"name":"Applicationes Mathematicae","volume":"19 1","pages":"79-93"},"PeriodicalIF":0.0,"publicationDate":"2016-01-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"91079087","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 unilateral contact problem with slip-dependent friction 具有滑移依赖摩擦的单侧接触问题
Applicationes Mathematicae Pub Date : 2016-01-01 DOI: 10.4064/am2258-11-2015
A. Touzaline
{"title":"A unilateral contact problem with slip-dependent friction","authors":"A. Touzaline","doi":"10.4064/am2258-11-2015","DOIUrl":"https://doi.org/10.4064/am2258-11-2015","url":null,"abstract":"We consider a mathematical model which describes a static contact between a nonlinear elastic body and an obstacle. The contact is modelled with Signorini’s conditions, associated with a slip-dependent version of Coulomb’s nonlocal friction law. We derive a variational formulation and prove its unique weak solvability. We also study the finite element approximation of the problem and obtain an optimal error estimate under extra regularity for the solution. Finally, we establish the convergence of an iterative method to the finite element problem.","PeriodicalId":52313,"journal":{"name":"Applicationes Mathematicae","volume":"22 1","pages":"105-116"},"PeriodicalIF":0.0,"publicationDate":"2016-01-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"77605512","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
The shortest confidence interval for proportion in finite populations 有限总体中比例的最短置信区间
Applicationes Mathematicae Pub Date : 2016-01-01 DOI: 10.4064/AM2297-7-2016
W. Zielinski
{"title":"The shortest confidence interval for proportion in finite populations","authors":"W. Zielinski","doi":"10.4064/AM2297-7-2016","DOIUrl":"https://doi.org/10.4064/AM2297-7-2016","url":null,"abstract":"","PeriodicalId":52313,"journal":{"name":"Applicationes Mathematicae","volume":"64 1","pages":"173-183"},"PeriodicalIF":0.0,"publicationDate":"2016-01-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"85672303","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
Left general fractional monotone approximation theory 左一般分数阶单调近似理论
Applicationes Mathematicae Pub Date : 2016-01-01 DOI: 10.4064/AM2264-12-2015
G. Anastassiou
{"title":"Left general fractional monotone approximation theory","authors":"G. Anastassiou","doi":"10.4064/AM2264-12-2015","DOIUrl":"https://doi.org/10.4064/AM2264-12-2015","url":null,"abstract":"","PeriodicalId":52313,"journal":{"name":"Applicationes Mathematicae","volume":"425 1","pages":"117-131"},"PeriodicalIF":0.0,"publicationDate":"2016-01-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"75674121","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: 4
A modified nonsymmetric rational block Lanczos method for model reduction in large scale LTI dynamical systems 大尺度LTI动力系统模型约简的改进非对称有理块Lanczos方法
Applicationes Mathematicae Pub Date : 2016-01-01 DOI: 10.4064/AM2302-5-2016
H. Barkouki, A. H. Bentbib, K. Jbilou
{"title":"A modified nonsymmetric rational block Lanczos method for model reduction in large scale LTI dynamical systems","authors":"H. Barkouki, A. H. Bentbib, K. Jbilou","doi":"10.4064/AM2302-5-2016","DOIUrl":"https://doi.org/10.4064/AM2302-5-2016","url":null,"abstract":"We propose an adaptive model reduction algorithm for computing a reduced-order model of dynamical multi-input and multi-output (MIMO) linear time independent (LTI) dynamical systems. The process is based on multipoint moment matching. Moreover, we develop new simple Lanczos-like equations for the rational block case, and we use them to derive simple residual error expressions. An adaptive method for choosing the interpolation points is also proposed. Finally, some numerical experiments are reported to show the effectiveness of the new adaptive modified rational block Lanczos (AMRBL) process when applied to stable linear LTI dynamical systems.","PeriodicalId":52313,"journal":{"name":"Applicationes Mathematicae","volume":"6 1","pages":"277-294"},"PeriodicalIF":0.0,"publicationDate":"2016-01-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"76123252","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
A note on invariant polynomials 关于不变多项式的注解
Applicationes Mathematicae Pub Date : 2016-01-01 DOI: 10.4064/am2164-12-2015
A. W. Davis
{"title":"A note on invariant polynomials","authors":"A. W. Davis","doi":"10.4064/am2164-12-2015","DOIUrl":"https://doi.org/10.4064/am2164-12-2015","url":null,"abstract":"","PeriodicalId":52313,"journal":{"name":"Applicationes Mathematicae","volume":"63 1","pages":"185-190"},"PeriodicalIF":0.0,"publicationDate":"2016-01-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"85295951","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
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