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Elliptic polytopes and invariant norms of linear operators 椭圆多边形与线性算子的不变范数
IF 1.7 2区 数学
Calcolo Pub Date : 2023-11-17 DOI: 10.1007/s10092-023-00547-z
Thomas Mejstrik, Valdimir Yu. Protasov
{"title":"Elliptic polytopes and invariant norms of linear operators","authors":"Thomas Mejstrik, Valdimir Yu. Protasov","doi":"10.1007/s10092-023-00547-z","DOIUrl":"https://doi.org/10.1007/s10092-023-00547-z","url":null,"abstract":"<p>Elliptic polytopes are convex hulls of several concentric plane ellipses in <span>({{mathbb {R}}}^d)</span>. They arise in applications as natural generalizations of usual polytopes. In particular, they define invariant convex bodies of linear operators, optimal Lyapunov norms for linear dynamical systems, etc. To construct elliptic polytopes one needs to decide whether a given ellipse is contained in the convex hull of other ellipses. We analyse the computational complexity of this problem and show that for <span>(d=2, 3)</span>, it admits an explicit solution. For larger <i>d</i>, two geometric methods for approximate solution are presented. Both use the convex optimization tools. The efficiency of the methods is demonstrated in two applications: the construction of extremal norms of linear operators and the computation of the joint spectral radius/Lyapunov exponent of a family of matrices.</p>","PeriodicalId":9522,"journal":{"name":"Calcolo","volume":null,"pages":null},"PeriodicalIF":1.7,"publicationDate":"2023-11-17","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"138525782","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":2,"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 linear algebra perspective on the random multi-block ADMM: the QP case 随机多块ADMM的线性代数透视:QP情况
IF 1.7 2区 数学
Calcolo Pub Date : 2023-11-15 DOI: 10.1007/s10092-023-00546-0
Stefano Cipolla, Jacek Gondzio
{"title":"A linear algebra perspective on the random multi-block ADMM: the QP case","authors":"Stefano Cipolla, Jacek Gondzio","doi":"10.1007/s10092-023-00546-0","DOIUrl":"https://doi.org/10.1007/s10092-023-00546-0","url":null,"abstract":"<p>Embedding randomization procedures in the Alternating Direction Method of Multipliers (ADMM) has recently attracted an increasing amount of interest as a remedy to the fact that the direct multi-block generalization of ADMM is not necessarily convergent. Even if, in practice, the introduction of such techniques could <i>mitigate</i> the diverging behaviour of the multi-block extension of ADMM, from the theoretical point of view, it can ensure just the <i>convergence in expectation</i>, which may not be a good indicator of its robustness and efficiency. In this work, analysing the strongly convex quadratic programming case from a linear algebra perspective, we interpret the block Gauss–Seidel sweep performed by the multi-block ADMM in the context of the inexact Augmented Lagrangian Method. Using the proposed analysis, we are able to outline an alternative technique to those present in the literature which, supported from stronger theoretical guarantees, is able to ensure the convergence of the multi-block generalization of the ADMM method.</p>","PeriodicalId":9522,"journal":{"name":"Calcolo","volume":null,"pages":null},"PeriodicalIF":1.7,"publicationDate":"2023-11-15","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"138513132","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":2,"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
Fast barycentric rational interpolations for complex functions with some singularities 具有奇异点的复函数的快速质心有理插值
IF 1.7 2区 数学
Calcolo Pub Date : 2023-11-15 DOI: 10.1007/s10092-023-00550-4
Shunfeng Yang, Shuhuang Xiang
{"title":"Fast barycentric rational interpolations for complex functions with some singularities","authors":"Shunfeng Yang, Shuhuang Xiang","doi":"10.1007/s10092-023-00550-4","DOIUrl":"https://doi.org/10.1007/s10092-023-00550-4","url":null,"abstract":"<p>Based on Cauchy’s integral formula and conformal maps, this paper presents a new method for constructing barycentric rational interpolation formulae for complex functions, which may contain singularities such as poles, branch cuts, or essential singularities. The resulting interpolations are pole-free, exponentially convergent, and numerically stable, requiring only <span>({mathcal {O}}(N))</span> operations. Inspired by the logarithm equilibrium potential, we introduce a Möbius transform to concentrate nodes to the vicinity of singularity to get a spectacular improvement on approximation quality. A thorough convergence analysis is provided, alongside numerous numerical examples that illustrate the theoretical results and demonstrate the accuracy and efficiency of the methodology. Meanwhile, the paper also discusses some applications of the method including the numerical solutions of boundary value problems and the zero locations of holomorphic functions.</p>","PeriodicalId":9522,"journal":{"name":"Calcolo","volume":null,"pages":null},"PeriodicalIF":1.7,"publicationDate":"2023-11-15","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"138525839","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":2,"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
On greedy randomized block Gauss–Seidel method with averaging for sparse linear least-squares problems 稀疏线性最小二乘问题的贪婪随机块高斯-塞德尔平均法
2区 数学
Calcolo Pub Date : 2023-11-01 DOI: 10.1007/s10092-023-00549-x
Yimou Liao, Tianxiu Lu
{"title":"On greedy randomized block Gauss–Seidel method with averaging for sparse linear least-squares problems","authors":"Yimou Liao, Tianxiu Lu","doi":"10.1007/s10092-023-00549-x","DOIUrl":"https://doi.org/10.1007/s10092-023-00549-x","url":null,"abstract":"","PeriodicalId":9522,"journal":{"name":"Calcolo","volume":null,"pages":null},"PeriodicalIF":0.0,"publicationDate":"2023-11-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"135714481","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":2,"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 posteriori analysis for a mixed formulation of the Stokes spectral problem Stokes谱问题混合公式的后验分析
2区 数学
Calcolo Pub Date : 2023-11-01 DOI: 10.1007/s10092-023-00548-y
Felipe Lepe, Jesus Vellojin
{"title":"A posteriori analysis for a mixed formulation of the Stokes spectral problem","authors":"Felipe Lepe, Jesus Vellojin","doi":"10.1007/s10092-023-00548-y","DOIUrl":"https://doi.org/10.1007/s10092-023-00548-y","url":null,"abstract":"","PeriodicalId":9522,"journal":{"name":"Calcolo","volume":null,"pages":null},"PeriodicalIF":0.0,"publicationDate":"2023-11-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"135714495","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":2,"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 Banach spaces-based mixed finite element method for the stationary convective Brinkman–Forchheimer problem 静止对流Brinkman-Forchheimer问题的基于Banach空间的混合有限元方法
2区 数学
Calcolo Pub Date : 2023-10-20 DOI: 10.1007/s10092-023-00544-2
Sergio Caucao, Gabriel N. Gatica, Luis F. Gatica
{"title":"A Banach spaces-based mixed finite element method for the stationary convective Brinkman–Forchheimer problem","authors":"Sergio Caucao, Gabriel N. Gatica, Luis F. Gatica","doi":"10.1007/s10092-023-00544-2","DOIUrl":"https://doi.org/10.1007/s10092-023-00544-2","url":null,"abstract":"","PeriodicalId":9522,"journal":{"name":"Calcolo","volume":null,"pages":null},"PeriodicalIF":0.0,"publicationDate":"2023-10-20","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"135513760","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":2,"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
Two-dimensional Jacobi pseudospectral quadrature solutions of two-dimensional fractional Volterra integral equations 二维分数阶Volterra积分方程的二维Jacobi伪谱正交解
2区 数学
Calcolo Pub Date : 2023-10-18 DOI: 10.1007/s10092-023-00545-1
A. K. Mittal
{"title":"Two-dimensional Jacobi pseudospectral quadrature solutions of two-dimensional fractional Volterra integral equations","authors":"A. K. Mittal","doi":"10.1007/s10092-023-00545-1","DOIUrl":"https://doi.org/10.1007/s10092-023-00545-1","url":null,"abstract":"","PeriodicalId":9522,"journal":{"name":"Calcolo","volume":null,"pages":null},"PeriodicalIF":0.0,"publicationDate":"2023-10-18","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"135823962","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":2,"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 weighted ADI scheme with variable time steps for diffusion-wave equations 扩散波方程的变时间步长加权ADI格式
2区 数学
Calcolo Pub Date : 2023-10-09 DOI: 10.1007/s10092-023-00543-3
Pin Lyu, Seakweng Vong
{"title":"A weighted ADI scheme with variable time steps for diffusion-wave equations","authors":"Pin Lyu, Seakweng Vong","doi":"10.1007/s10092-023-00543-3","DOIUrl":"https://doi.org/10.1007/s10092-023-00543-3","url":null,"abstract":"","PeriodicalId":9522,"journal":{"name":"Calcolo","volume":null,"pages":null},"PeriodicalIF":0.0,"publicationDate":"2023-10-09","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"135095623","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":2,"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
Preconditioning of discrete state- and control-constrained optimal control convection-diffusion problems 离散状态和控制约束的最优控制对流扩散问题的预处理
2区 数学
Calcolo Pub Date : 2023-10-08 DOI: 10.1007/s10092-023-00542-4
Ivo Dravins, Maya Neytcheva
{"title":"Preconditioning of discrete state- and control-constrained optimal control convection-diffusion problems","authors":"Ivo Dravins, Maya Neytcheva","doi":"10.1007/s10092-023-00542-4","DOIUrl":"https://doi.org/10.1007/s10092-023-00542-4","url":null,"abstract":"Abstract We consider the iterative solution of algebraic systems, arising in optimal control problems constrained by a partial differential equation with additional box constraints on the state and the control variables, and sparsity imposed on the control. A nonsymmetric two-by-two block preconditioner is analysed and tested for a wide range of problem, regularization and discretization parameters. The constraint equation characterizes convection-diffusion processes.","PeriodicalId":9522,"journal":{"name":"Calcolo","volume":null,"pages":null},"PeriodicalIF":0.0,"publicationDate":"2023-10-08","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"135198276","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":2,"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 numerical method for analysis and simulation of diffusive viscous wave equations with variable coefficients on polygonal meshes 多角形网格上变系数扩散粘性波动方程的数值分析与模拟
2区 数学
Calcolo Pub Date : 2023-10-06 DOI: 10.1007/s10092-023-00541-5
Naresh Kumar, Bhupen Deka
{"title":"A numerical method for analysis and simulation of diffusive viscous wave equations with variable coefficients on polygonal meshes","authors":"Naresh Kumar, Bhupen Deka","doi":"10.1007/s10092-023-00541-5","DOIUrl":"https://doi.org/10.1007/s10092-023-00541-5","url":null,"abstract":"","PeriodicalId":9522,"journal":{"name":"Calcolo","volume":null,"pages":null},"PeriodicalIF":0.0,"publicationDate":"2023-10-06","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"135346594","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":2,"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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