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Generalized Drazin Invertibility of Operator Matrices 算子矩阵的广义Drazin可逆性
IF 1.2 4区 数学
Numerical Functional Analysis and Optimization Pub Date : 2022-10-28 DOI: 10.1080/01630563.2022.2137811
Aymen Bahloul, I. Walha
{"title":"Generalized Drazin Invertibility of Operator Matrices","authors":"Aymen Bahloul, I. Walha","doi":"10.1080/01630563.2022.2137811","DOIUrl":"https://doi.org/10.1080/01630563.2022.2137811","url":null,"abstract":"Abstract In this paper, we investigate the generalized Drazin invertibility of upper triangular operator matrices acting on Banach spaces. Among other things, we explicit the defect set with respect to the local spectral theory. Moreover, we exhibit some sufficient conditions which assure that the generalized Drazin spectrum of a 3 × 3 upper triangular block operator matrix is the union of its diagonal entries spectra.","PeriodicalId":54707,"journal":{"name":"Numerical Functional Analysis and Optimization","volume":"43 1","pages":"1836 - 1847"},"PeriodicalIF":1.2,"publicationDate":"2022-10-28","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"49431605","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":4,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
引用次数: 1
On the Eigenstructure of the Modified Bernstein Operators 关于修正Bernstein算子的特征结构
IF 1.2 4区 数学
Numerical Functional Analysis and Optimization Pub Date : 2022-10-28 DOI: 10.1080/01630563.2022.2136695
Övgü Gürel Yılmaz, Sofiya Ostrovska, M. Turan
{"title":"On the Eigenstructure of the Modified Bernstein Operators","authors":"Övgü Gürel Yılmaz, Sofiya Ostrovska, M. Turan","doi":"10.1080/01630563.2022.2136695","DOIUrl":"https://doi.org/10.1080/01630563.2022.2136695","url":null,"abstract":"Abstract Starting from the well-known work of Cooper and Waldron published in 2000, the eigenstructure of various Bernstein-type operators has been investigated by many researchers. In this work, the eigenvalues and eigenvectors of the modified Bernstein operators Qn have been studied. These operators were introduced by S. N. Bernstein himself, in 1932, for the purpose of accelerating the approximation rate for smooth functions. Here, the explicit formulae for the eigenvalues and corresponding eigenpolynomials together with their limiting behavior are established. The results show that although some outcomes are similar to those for the Bernstein operators, there are essentially different ones as well.","PeriodicalId":54707,"journal":{"name":"Numerical Functional Analysis and Optimization","volume":"43 1","pages":"1821 - 1835"},"PeriodicalIF":1.2,"publicationDate":"2022-10-28","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"44924578","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":4,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
引用次数: 0
Properties of the Solution Set of a Class of Mixed Variational Inqualities 一类混合变分不等式解集的性质
IF 1.2 4区 数学
Numerical Functional Analysis and Optimization Pub Date : 2022-10-21 DOI: 10.1080/01630563.2022.2135102
Yang Xu, Zhenghai Huang
{"title":"Properties of the Solution Set of a Class of Mixed Variational Inqualities","authors":"Yang Xu, Zhenghai Huang","doi":"10.1080/01630563.2022.2135102","DOIUrl":"https://doi.org/10.1080/01630563.2022.2135102","url":null,"abstract":"Abstract In this paper, we investigate a class of mixed variational inequalities on nonempty closed convex subsets of real Euclidean spaces. One of the mappings involved is lower semicontinuous and the other is weakly homogeneous. After discussing the boundedness for the solution set (if it is nonempty) of the problem, we focus on the nonemptiness and compactness of the solution set. Two new results on the nonemptiness and compactness of the solution set of the problem are established, and some examples are used to compare the results with those in the literature. It can be seen that new results improve some known related results.","PeriodicalId":54707,"journal":{"name":"Numerical Functional Analysis and Optimization","volume":"43 1","pages":"1779 - 1800"},"PeriodicalIF":1.2,"publicationDate":"2022-10-21","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"49360770","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":4,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
引用次数: 0
Phase Retrieval from Linear Canonical Transforms 基于线性正则变换的相位检索
IF 1.2 4区 数学
Numerical Functional Analysis and Optimization Pub Date : 2022-10-19 DOI: 10.1080/01630563.2022.2132511
Yang Chen, Na Qu
{"title":"Phase Retrieval from Linear Canonical Transforms","authors":"Yang Chen, Na Qu","doi":"10.1080/01630563.2022.2132511","DOIUrl":"https://doi.org/10.1080/01630563.2022.2132511","url":null,"abstract":"Abstract The classical phase retrieval problem aims to recover an unknown function from the Fourier magnitudes. The linear canonical transform has a more generalized form of the well-known (fractional) Fourier transform and a wide range of engineering applications such as optics and quantum mechanism. In this paper, we consider the linear canonic phase retrieval problem of determining a function from the magnitudes of the linear canonic transforms. We show that a compactly supported function f can be determined, up to a global phase, from the magnitudes of multiple linear canonic transforms, where is a class of real unimodular matrices. It generalizes the results of phase retrieval from multiple fractional Fourier transforms. On the other hand, we show that a compactly supported function f can be determined, up to a global phase, from the interference linear canonic magnitudes and where Moreover, if the ambiguity of conjugate reflection is taken into account, the compactly supported function f can be determined, up to a rotation and conjugate reflection, from the linear canonic magnitudes and","PeriodicalId":54707,"journal":{"name":"Numerical Functional Analysis and Optimization","volume":"43 1","pages":"1760 - 1777"},"PeriodicalIF":1.2,"publicationDate":"2022-10-19","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"43273783","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":4,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
引用次数: 1
Combined Legendre Spectral-Finite Element Methods for Two-Dimensional Fredholm Integral Equations of the Second Kind 二维第二类Fredholm积分方程的联合Legendre谱-有限元方法
IF 1.2 4区 数学
Numerical Functional Analysis and Optimization Pub Date : 2022-10-19 DOI: 10.1080/01630563.2022.2135540
B. L. Panigrahi
{"title":"Combined Legendre Spectral-Finite Element Methods for Two-Dimensional Fredholm Integral Equations of the Second Kind","authors":"B. L. Panigrahi","doi":"10.1080/01630563.2022.2135540","DOIUrl":"https://doi.org/10.1080/01630563.2022.2135540","url":null,"abstract":"Abstract In this paper, we will discuss on the Combined Legendre spectral-Finite element methods (CLSFEM) for the two-dimensional Fredholm integral equations with smooth kernel on the Banach spaces and the corresponding eigenvalue problem. In these methods, the approximated finite dimensional space is the cartesian product of spline space and Legendre polynomial space. The problem is approximated by the CLSFEM using orthogonal projection, which projects from the Banach space into the finite dimensional space. The convergence analysis for both Fredholm integral equations and the corresponding eigenvalue problem will be discussed in both L 2 and norms. The numerical results will be shown to validate the theoretical estimate.","PeriodicalId":54707,"journal":{"name":"Numerical Functional Analysis and Optimization","volume":"43 1","pages":"1801 - 1820"},"PeriodicalIF":1.2,"publicationDate":"2022-10-19","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"48584640","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":4,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
引用次数: 0
Second-Order Optimality Conditions for Strict Pareto Minima and Weak Efficiency for Nonsmooth Constrained Vector Equilibrium Problems 严格Pareto极小的二阶最优性条件和非光滑约束向量平衡问题的弱有效性
IF 1.2 4区 数学
Numerical Functional Analysis and Optimization Pub Date : 2022-10-17 DOI: 10.1080/01630563.2022.2132510
T. Su, D. Luu
{"title":"Second-Order Optimality Conditions for Strict Pareto Minima and Weak Efficiency for Nonsmooth Constrained Vector Equilibrium Problems","authors":"T. Su, D. Luu","doi":"10.1080/01630563.2022.2132510","DOIUrl":"https://doi.org/10.1080/01630563.2022.2132510","url":null,"abstract":"Abstract In this article, some types of lower and upper second-order strictly pseudoconvexity are provided for establishing sufficient conditions for the second-order strict local Pareto minima of nonsmooth vector equilibrium problem with set, inequality and equality constraints. Based on the notion of Gerstewitz mappings, some Kuhn-Tucker-type multiplier rules for the strict local Pareto minima of such problem are obtained. We also construct the second-order constraint qualification in terms of first- and second-order directional derivatives of the (CQ) and (CQ1) types. Using this constraint qualifications, some second-order primal and dual necessary optimality conditions in terms of second-order upper and lower Dini directional derivatives for such minima are derived. Under suitable assumptions on the lower and upper strictly pseudoconvexity of order two of objective and constraint functions, second-order necessary optimality conditions become sufficient optimality conditions to such problem. Some illustrative examples are also given for our findings.","PeriodicalId":54707,"journal":{"name":"Numerical Functional Analysis and Optimization","volume":"43 1","pages":"1732 - 1759"},"PeriodicalIF":1.2,"publicationDate":"2022-10-17","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"44367351","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":4,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
引用次数: 0
Error Estimates for Approximate Solutions to Seminlinear Elliptic Optimal Control Problems with Nonlinear and Mixed Constraints 非线性混合约束半线性椭圆型最优控制问题近似解的误差估计
IF 1.2 4区 数学
Numerical Functional Analysis and Optimization Pub Date : 2022-09-27 DOI: 10.1080/01630563.2022.2124271
B. T. Kien, N. Tuan
{"title":"Error Estimates for Approximate Solutions to Seminlinear Elliptic Optimal Control Problems with Nonlinear and Mixed Constraints","authors":"B. T. Kien, N. Tuan","doi":"10.1080/01630563.2022.2124271","DOIUrl":"https://doi.org/10.1080/01630563.2022.2124271","url":null,"abstract":"Abstract This paper gives some sufficient conditions for convergence of approximate solutions to seminlinear elliptic optimal control problems with mixed pointwise constraints. We build discrete optimal control problems by the finite element method in type of the full control discretization. We show that if the strictly second-order sufficient condition is valid, then some error estimates between approximate solutions of discrete optimal control problems and optimal solutions of the original problem are obtained.","PeriodicalId":54707,"journal":{"name":"Numerical Functional Analysis and Optimization","volume":"43 1","pages":"1672 - 1706"},"PeriodicalIF":1.2,"publicationDate":"2022-09-27","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"49187155","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":4,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
引用次数: 2
The Complete Solution of the Construction Problem of Infinite Frames with Given Redundancy 具有给定冗余的无限框架构造问题的完全解
IF 1.2 4区 数学
Numerical Functional Analysis and Optimization Pub Date : 2022-09-24 DOI: 10.1080/01630563.2022.2124270
M. A. Hasankhani Fard
{"title":"The Complete Solution of the Construction Problem of Infinite Frames with Given Redundancy","authors":"M. A. Hasankhani Fard","doi":"10.1080/01630563.2022.2124270","DOIUrl":"https://doi.org/10.1080/01630563.2022.2124270","url":null,"abstract":"Abstract It is constructed infinite frames with some given redundancy. In this paper, the solution of the construction problem of infinite frames with given redundancy, is completed. More precisely, all possible infinite frame redundancies are characterized.","PeriodicalId":54707,"journal":{"name":"Numerical Functional Analysis and Optimization","volume":"43 1","pages":"1660 - 1671"},"PeriodicalIF":1.2,"publicationDate":"2022-09-24","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"42282865","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":4,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
引用次数: 0
A Mehrotra Type Predictor-Corrector Interior-Point Method for -HLCP -HLCP的Mehrotra型预测校正内点法
IF 1.2 4区 数学
Numerical Functional Analysis and Optimization Pub Date : 2022-09-21 DOI: 10.1080/01630563.2022.2123818
N. Hazzam, Z. Kebbiche
{"title":"A Mehrotra Type Predictor-Corrector Interior-Point Method for -HLCP","authors":"N. Hazzam, Z. Kebbiche","doi":"10.1080/01630563.2022.2123818","DOIUrl":"https://doi.org/10.1080/01630563.2022.2123818","url":null,"abstract":"Abstract In this article, a new variant of Mehrotra type-predictor-corrector algorithm is proposed for -horizontal linear complementarity problem. We demonstrate the theoretical efficiency of this algorithm by showing its polynomial complexity. The iteration bound is given by We test the practical efficiency and the validity of our algorithm by running some computational tests.","PeriodicalId":54707,"journal":{"name":"Numerical Functional Analysis and Optimization","volume":"43 1","pages":"1647 - 1659"},"PeriodicalIF":1.2,"publicationDate":"2022-09-21","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"42389841","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":4,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
引用次数: 0
Numerical Dynamics of Integrodifference Equations: Hierarchies of Invariant Bundles in Lp (Ω) 积分差分方程的数值动力学：Lp（Ω）中不变丛的层次
IF 1.2 4区 数学
Numerical Functional Analysis and Optimization Pub Date : 2022-09-05 DOI: 10.1080/01630563.2023.2189458
C. Pötzsche
{"title":"Numerical Dynamics of Integrodifference Equations: Hierarchies of Invariant Bundles in Lp (Ω)","authors":"C. Pötzsche","doi":"10.1080/01630563.2023.2189458","DOIUrl":"https://doi.org/10.1080/01630563.2023.2189458","url":null,"abstract":"Abstract We study how the “full hierarchy” of invariant manifolds for nonautonomous integrodifference equations on the Banach spaces of p-integrable functions behaves under spatial discretization of Galerkin type. These manifolds include the classical stable, center-stable, center, center-unstable and unstable ones, and can be represented as graphs of -functions. For kernels with a smoothing property, our main result establishes closeness of these graphs in the -topology under numerical discretizations preserving the convergence order of the method. It is formulated in a quantitative fashion and technically results from a general perturbation theorem on the existence of invariant bundles (i.e. nonautonomous invariant manifolds).","PeriodicalId":54707,"journal":{"name":"Numerical Functional Analysis and Optimization","volume":"44 1","pages":"653 - 686"},"PeriodicalIF":1.2,"publicationDate":"2022-09-05","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"46123629","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":4,"RegionCategory":"数学","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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