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Succinct obituary in memoriam of Joos Heintz 简练的讣告，纪念乔·海因茨
IF 1.8 2区 数学
Journal of Complexity Pub Date : 2024-11-29 DOI: 10.1016/j.jco.2024.101919
Luis M. Pardo
{"title":"Succinct obituary in memoriam of Joos Heintz","authors":"Luis M. Pardo","doi":"10.1016/j.jco.2024.101919","DOIUrl":"10.1016/j.jco.2024.101919","url":null,"abstract":"","PeriodicalId":50227,"journal":{"name":"Journal of Complexity","volume":"87 ","pages":"Article 101919"},"PeriodicalIF":1.8,"publicationDate":"2024-11-29","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"142742866","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
Direct estimates for adaptive time-stepping finite element methods 自适应时步有限元法的直接估计
IF 1.8 2区 数学
Journal of Complexity Pub Date : 2024-11-28 DOI: 10.1016/j.jco.2024.101918
Marcelo Actis , Fernando Gaspoz , Pedro Morin , Cornelia Schneider , Nick Schneider
{"title":"Direct estimates for adaptive time-stepping finite element methods","authors":"Marcelo Actis ,&nbsp;Fernando Gaspoz ,&nbsp;Pedro Morin ,&nbsp;Cornelia Schneider ,&nbsp;Nick Schneider","doi":"10.1016/j.jco.2024.101918","DOIUrl":"10.1016/j.jco.2024.101918","url":null,"abstract":"<div><div>We study direct estimates for adaptive time-stepping finite element methods for time-dependent partial differential equations. Our results generalize previous findings from “On approximation classes for adaptive time-stepping finite element methods” by Actis et al. (2023), where the approximation error was only measured in <span><math><msub><mrow><mi>L</mi></mrow><mrow><mn>2</mn></mrow></msub><mo>(</mo><mo>[</mo><mn>0</mn><mo>,</mo><mi>T</mi><mo>]</mo><mo>,</mo><msub><mrow><mi>L</mi></mrow><mrow><mn>2</mn></mrow></msub><mo>(</mo><mi>Ω</mi><mo>)</mo><mo>)</mo></math></span>. In particular, we now also cover the error norms <span><math><msub><mrow><mi>L</mi></mrow><mrow><mo>∞</mo></mrow></msub><mo>(</mo><mo>[</mo><mn>0</mn><mo>,</mo><mi>T</mi><mo>]</mo><mo>,</mo><msub><mrow><mi>L</mi></mrow><mrow><mn>2</mn></mrow></msub><mo>(</mo><mi>Ω</mi><mo>)</mo><mo>)</mo></math></span> and <span><math><msub><mrow><mi>L</mi></mrow><mrow><mn>2</mn></mrow></msub><mo>(</mo><mo>[</mo><mn>0</mn><mo>,</mo><mi>T</mi><mo>]</mo><mo>,</mo><msup><mrow><mi>H</mi></mrow><mrow><mn>1</mn></mrow></msup><mo>(</mo><mi>Ω</mi><mo>)</mo><mo>)</mo></math></span> which are more natural in this context.</div></div>","PeriodicalId":50227,"journal":{"name":"Journal of Complexity","volume":"87 ","pages":"Article 101918"},"PeriodicalIF":1.8,"publicationDate":"2024-11-28","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"143180611","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":2,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"OA","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
引用次数: 0
Stefan Heinrich is the Winner of the 2024 Best Paper Award of the Journal of Complexity 斯特凡-海因里希荣获《复杂性期刊》2024 年度最佳论文奖
IF 1.8 2区 数学
Journal of Complexity Pub Date : 2024-11-05 DOI: 10.1016/j.jco.2024.101905
Erich Novak, Mario Ullrich, Jan Vybíral
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引用次数: 0
Best Paper Award of the Journal of Complexity 复杂性期刊》最佳论文奖
IF 1.8 2区 数学
Journal of Complexity Pub Date : 2024-11-05 DOI: 10.1016/j.jco.2024.101904
{"title":"Best Paper Award of the Journal of Complexity","authors":"","doi":"10.1016/j.jco.2024.101904","DOIUrl":"10.1016/j.jco.2024.101904","url":null,"abstract":"","PeriodicalId":50227,"journal":{"name":"Journal of Complexity","volume":"86 ","pages":"Article 101904"},"PeriodicalIF":1.8,"publicationDate":"2024-11-05","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"142586491","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 two-point Newton-like method of optimal fourth order convergence for systems of nonlinear equations 非线性方程系统最优四阶收敛的类似牛顿的两点法
IF 1.8 2区 数学
Journal of Complexity Pub Date : 2024-11-05 DOI: 10.1016/j.jco.2024.101907
Harmandeep Singh , Janak Raj Sharma
{"title":"A two-point Newton-like method of optimal fourth order convergence for systems of nonlinear equations","authors":"Harmandeep Singh ,&nbsp;Janak Raj Sharma","doi":"10.1016/j.jco.2024.101907","DOIUrl":"10.1016/j.jco.2024.101907","url":null,"abstract":"<div><div>A two-step Newton-like method is proposed to efficiently solve the systems of nonlinear equations. Extending Newton scheme to a next step as weighted-Newton iteration, the proposed iteration scheme shows optimal fourth order of convergence. The primary objective in formulating the method is to keep the computational efficiency as high as possible. In this context, the efficiency analysis is thoroughly examined using a systematic approach, wherein the efficiency index of the new method is compared with those of existing methods of comparable complexity. Numerical experimentation is performed to investigate the computational efficacy of the developed method. Results indicate higher efficiency and numerical precision in comparison to the existing counterparts.</div></div>","PeriodicalId":50227,"journal":{"name":"Journal of Complexity","volume":"86 ","pages":"Article 101907"},"PeriodicalIF":1.8,"publicationDate":"2024-11-05","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"142656796","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
Combinatorial constructions of separating codes 分离密码的组合构造
IF 1.8 2区 数学
Journal of Complexity Pub Date : 2024-10-31 DOI: 10.1016/j.jco.2024.101906
Marcel Fernández , John Livieratos , Sebastià Martín
{"title":"Combinatorial constructions of separating codes","authors":"Marcel Fernández ,&nbsp;John Livieratos ,&nbsp;Sebastià Martín","doi":"10.1016/j.jco.2024.101906","DOIUrl":"10.1016/j.jco.2024.101906","url":null,"abstract":"<div><div>This paper presents an algorithmic approach to the construction of separating codes. In the first part of the work, the Lovász Local Lemma is used to obtain a lower bound on the code rate. This lower bound matches the previously best-known lower bound. In the second part, it is shown how the technique used in proving the lower bound leads to an algorithm that outputs an instance of a separating code. Moreover, the implications of the algorithm regarding computational complexity are considered. The discussion ends by presenting explicit separating codes with polynomial computational complexity in the length of the code, with rate that improves previously known constructions.</div></div>","PeriodicalId":50227,"journal":{"name":"Journal of Complexity","volume":"86 ","pages":"Article 101906"},"PeriodicalIF":1.8,"publicationDate":"2024-10-31","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"142656797","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
Matthieu Dolbeault is the winner of the 2024 Joseph F. Traub Information-Based Complexity Young Researcher Award 马蒂厄-多尔贝奥（Matthieu Dolbeault）是 2024 年约瑟夫-特劳布基于信息的复杂性青年研究员奖（Joseph F. Traub Information-Based Complexity Young Researcher Award）的获得者。
IF 1.8 2区 数学
Journal of Complexity Pub Date : 2024-10-22 DOI: 10.1016/j.jco.2024.101902
Erich Novak, Kateryna Pozharska, Mathias Sonnleitner, Michaela Szölgyenyi, Henryk Woźniakowski
{"title":"Matthieu Dolbeault is the winner of the 2024 Joseph F. Traub Information-Based Complexity Young Researcher Award","authors":"Erich Novak,&nbsp;Kateryna Pozharska,&nbsp;Mathias Sonnleitner,&nbsp;Michaela Szölgyenyi,&nbsp;Henryk Woźniakowski","doi":"10.1016/j.jco.2024.101902","DOIUrl":"10.1016/j.jco.2024.101902","url":null,"abstract":"","PeriodicalId":50227,"journal":{"name":"Journal of Complexity","volume":"86 ","pages":"Article 101902"},"PeriodicalIF":1.8,"publicationDate":"2024-10-22","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"142525769","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
Optimal recovery of linear operators from information of random functions 从随机函数信息中优化恢复线性算子
IF 1.8 2区 数学
Journal of Complexity Pub Date : 2024-10-21 DOI: 10.1016/j.jco.2024.101903
K.Yu. Osipenko
{"title":"Optimal recovery of linear operators from information of random functions","authors":"K.Yu. Osipenko","doi":"10.1016/j.jco.2024.101903","DOIUrl":"10.1016/j.jco.2024.101903","url":null,"abstract":"<div><div>The paper concerns problems of the recovery of linear operators defined on sets of functions from information of these functions given with stochastic errors. The constructed optimal recovery methods, in general, do not use all the available information. As a consequence, optimal methods are obtained for recovering derivatives of functions from Sobolev classes by the information of their Fourier transforms given with stochastic errors. A similar problem is considered for solutions of the heat equation.</div></div>","PeriodicalId":50227,"journal":{"name":"Journal of Complexity","volume":"86 ","pages":"Article 101903"},"PeriodicalIF":1.8,"publicationDate":"2024-10-21","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"142527379","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
Intractability results for integration in tensor product spaces 张量乘空间积分的难解性结果
IF 1.8 2区 数学
Journal of Complexity Pub Date : 2024-10-16 DOI: 10.1016/j.jco.2024.101901
Erich Novak , Friedrich Pillichshammer
{"title":"Intractability results for integration in tensor product spaces","authors":"Erich Novak ,&nbsp;Friedrich Pillichshammer","doi":"10.1016/j.jco.2024.101901","DOIUrl":"10.1016/j.jco.2024.101901","url":null,"abstract":"<div><div>We prove lower bounds on the worst-case error of numerical integration in tensor product spaces. The information complexity is the minimal number <em>N</em> of function evaluations that is necessary such that the <em>N</em>-th minimal error is less than a factor <em>ε</em> times the initial error, i.e., the error for <span><math><mi>N</mi><mo>=</mo><mn>0</mn></math></span>, where <em>ε</em> belongs to <span><math><mo>(</mo><mn>0</mn><mo>,</mo><mn>1</mn><mo>)</mo></math></span>. We are interested to which extent the information complexity depends on the number <em>d</em> of variables of the integrands. If the information complexity grows exponentially fast in <em>d</em>, then the integration problem is said to suffer from the curse of dimensionality.</div><div>Under the assumption of the existence of a worst-case function for the uni-variate problem, we present two methods for providing lower bounds on the information complexity. The first method is based on a suitable decomposition of the worst-case function and can be seen as a generalization of the method of decomposable reproducing kernels. The second method, although only applicable for positive quadrature rules, does not require a suitable decomposition of the worst-case function. Rather, it is based on a spline approximation of the worst-case function and can be used for analytic functions. Several applications of both methods are presented.</div></div>","PeriodicalId":50227,"journal":{"name":"Journal of Complexity","volume":"86 ","pages":"Article 101901"},"PeriodicalIF":1.8,"publicationDate":"2024-10-16","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"142445798","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":2,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"OA","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
引用次数: 0
Kernel multigrid on manifolds 流形上的核多网格
IF 1.8 2区 数学
Journal of Complexity Pub Date : 2024-10-09 DOI: 10.1016/j.jco.2024.101900
Thomas Hangelbroek , Christian Rieger
{"title":"Kernel multigrid on manifolds","authors":"Thomas Hangelbroek ,&nbsp;Christian Rieger","doi":"10.1016/j.jco.2024.101900","DOIUrl":"10.1016/j.jco.2024.101900","url":null,"abstract":"<div><div>Kernel methods for solving partial differential equations work coordinate-free on the surface and yield high approximation rates for smooth solutions. Localized Lagrange bases have proven to alleviate the computational complexity of usual kernel methods for data fitting problems, but the efficient numerical solution of the ill-conditioned linear systems of equations arising from kernel-based Galerkin solutions to PDEs is a challenging problem which has not been addressed in the literature so far. In this article we apply the framework of the geometric multigrid method with a <span><math><mi>τ</mi><mo>≥</mo><mn>2</mn></math></span>-cycle to scattered, quasi-uniform point clouds on the surface. We show that the resulting solver can be accelerated by using the Lagrange function decay and obtain satisfying convergence rates by a rigorous analysis. In particular, we show that the computational cost of the linear solver scales log-linear in the degrees of freedom.</div></div>","PeriodicalId":50227,"journal":{"name":"Journal of Complexity","volume":"86 ","pages":"Article 101900"},"PeriodicalIF":1.8,"publicationDate":"2024-10-09","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"142527392","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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