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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
{"title":"Stefan Heinrich is the Winner of the 2024 Best Paper Award of the Journal of Complexity","authors":"Erich Novak, Mario Ullrich, Jan Vybíral","doi":"10.1016/j.jco.2024.101905","DOIUrl":"10.1016/j.jco.2024.101905","url":null,"abstract":"","PeriodicalId":50227,"journal":{"name":"Journal of Complexity","volume":null,"pages":null},"PeriodicalIF":1.8,"publicationDate":"2024-11-05","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"142586490","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
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":null,"pages":null},"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
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, Kateryna Pozharska, Mathias Sonnleitner, Michaela Szölgyenyi, 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":null,"pages":null},"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":null,"pages":null},"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":null,"pages":null},"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":null,"pages":null},"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
Space-filling designs on Riemannian manifolds 黎曼流形上的空间填充设计
IF 1.8 2区 数学
Journal of Complexity Pub Date : 2024-09-24 DOI: 10.1016/j.jco.2024.101899
Mingyao Ai , Yunfan Yang , Xiangshun Kong
{"title":"Space-filling designs on Riemannian manifolds","authors":"Mingyao Ai ,&nbsp;Yunfan Yang ,&nbsp;Xiangshun Kong","doi":"10.1016/j.jco.2024.101899","DOIUrl":"10.1016/j.jco.2024.101899","url":null,"abstract":"<div><div>This paper proposes a new approach to generating space-filling designs over Riemannian manifolds by using a Hilbert curve. Different from ordinary Euclidean spaces, a novel transformation is constructed to link the uniform distribution over a Riemannian manifold and that over its parameter space. Using this transformation, the uniformity of the design points in the sense of Riemannian volume measure can be guaranteed by the intrinsic measure preserving property of the Hilbert curve. It is proved that these generated designs are not only asymptotically optimal under minimax and maximin distance criteria, but also perform well in minimizing the Wasserstein distance from the target distribution and controlling the estimation error in numerical integration. Furthermore, an efficient algorithm is developed for numerical generation of these space-filling designs. The advantages of the new approach are verified through numerical simulations.</div></div>","PeriodicalId":50227,"journal":{"name":"Journal of Complexity","volume":null,"pages":null},"PeriodicalIF":1.8,"publicationDate":"2024-09-24","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"142319731","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 the number of solutions to a random instance of the permuted kernel problem 关于包络核问题随机实例的解数
IF 1.8 2区 数学
Journal of Complexity Pub Date : 2024-09-24 DOI: 10.1016/j.jco.2024.101898
Carlo Sanna
{"title":"On the number of solutions to a random instance of the permuted kernel problem","authors":"Carlo Sanna","doi":"10.1016/j.jco.2024.101898","DOIUrl":"10.1016/j.jco.2024.101898","url":null,"abstract":"<div><div>The <em>Permuted Kernel Problem</em> (PKP) is a problem in linear algebra that was first introduced by Shamir in 1989. Roughly speaking, given an <span><math><mi>ℓ</mi><mo>×</mo><mi>m</mi></math></span> matrix <strong><em>A</em></strong> and an <span><math><mi>m</mi><mo>×</mo><mn>1</mn></math></span> vector <strong><em>b</em></strong> over a finite field of <em>q</em> elements <span><math><msub><mrow><mi>F</mi></mrow><mrow><mi>q</mi></mrow></msub></math></span>, the PKP asks to find an <span><math><mi>m</mi><mo>×</mo><mi>m</mi></math></span> permutation matrix <strong><em>π</em></strong> such that <span><math><mi>π</mi><mi>b</mi></math></span> belongs to the kernel of <strong><em>A</em></strong>. In recent years, several post-quantum digital signature schemes whose security can be provably reduced to the hardness of solving random instances of the PKP have been proposed. In this regard, it is important to know the expected number of solutions to a random instance of the PKP in terms of the parameters <span><math><mi>q</mi><mo>,</mo><mi>ℓ</mi><mo>,</mo><mi>m</mi></math></span>. Previous works have heuristically estimated the expected number of solutions to be <span><math><mi>m</mi><mo>!</mo><mo>/</mo><msup><mrow><mi>q</mi></mrow><mrow><mi>ℓ</mi></mrow></msup></math></span>.</div><div>We provide, and rigorously prove, exact formulas for the expected number of solutions to a random instance of the PKP and the related <em>Inhomogeneous Permuted Kernel Problem</em> (IPKP), considering two natural ways of generating random instances.</div></div>","PeriodicalId":50227,"journal":{"name":"Journal of Complexity","volume":null,"pages":null},"PeriodicalIF":1.8,"publicationDate":"2024-09-24","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://www.sciencedirect.com/science/article/pii/S0885064X2400075X/pdfft?md5=939873f4b51043507214927d47f2bb37&pid=1-s2.0-S0885064X2400075X-main.pdf","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"142314359","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
Convergence analysis of iteratively regularized Landweber iteration with uniformly convex constraints in Banach spaces 巴拿赫空间中具有均匀凸约束条件的迭代正则化 Landweber 迭代的收敛性分析
IF 1.8 2区 数学
Journal of Complexity Pub Date : 2024-09-13 DOI: 10.1016/j.jco.2024.101897
Gaurav Mittal , Harshit Bajpai , Ankik Kumar Giri
{"title":"Convergence analysis of iteratively regularized Landweber iteration with uniformly convex constraints in Banach spaces","authors":"Gaurav Mittal ,&nbsp;Harshit Bajpai ,&nbsp;Ankik Kumar Giri","doi":"10.1016/j.jco.2024.101897","DOIUrl":"10.1016/j.jco.2024.101897","url":null,"abstract":"<div><p>In Banach spaces, the convergence analysis of iteratively regularized Landweber iteration (IRLI) is recently studied via conditional stability estimates. But the formulation of IRLI does not include general non-smooth convex penalty functionals, which is essential to capture special characteristics of the sought solution. In this paper, we formulate a generalized form of IRLI so that its formulation includes general non-smooth uniformly convex penalty functionals. We study the convergence analysis and derive the convergence rates of the generalized method solely via conditional stability estimates in Banach spaces for both the perturbed and unperturbed data. We also discuss few examples of inverse problems on which our method is applicable.</p></div>","PeriodicalId":50227,"journal":{"name":"Journal of Complexity","volume":null,"pages":null},"PeriodicalIF":1.8,"publicationDate":"2024-09-13","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://www.sciencedirect.com/science/article/pii/S0885064X24000748/pdfft?md5=5ae8eeac0a143f493ee150c18db69cf1&pid=1-s2.0-S0885064X24000748-main.pdf","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"142240454","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
High-efficiency parametric iterative schemes for solving nonlinear equations with and without memory 求解有内存和无内存非线性方程的高效参数迭代方案
IF 1.8 2区 数学
Journal of Complexity Pub Date : 2024-09-11 DOI: 10.1016/j.jco.2024.101896
Raziyeh Erfanifar, Masoud Hajarian
{"title":"High-efficiency parametric iterative schemes for solving nonlinear equations with and without memory","authors":"Raziyeh Erfanifar,&nbsp;Masoud Hajarian","doi":"10.1016/j.jco.2024.101896","DOIUrl":"10.1016/j.jco.2024.101896","url":null,"abstract":"<div><p>Many practical problems, such as the Malthusian population growth model, eigenvalue computations for matrices, and solving the Van der Waals' ideal gas equation, inherently involve nonlinearities. This paper initially introduces a two-parameter iterative scheme with a convergence order of two. Building on this, a three-parameter scheme with a convergence order of four is proposed. Then we extend these schemes into higher-order schemes with memory using Newton's interpolation, achieving an upper bound for the efficiency index of <span><math><msup><mrow><mn>7.88748</mn></mrow><mrow><mfrac><mrow><mn>1</mn></mrow><mrow><mn>3</mn></mrow></mfrac></mrow></msup><mo>≈</mo><mn>1.99057</mn></math></span>. Finally, we validate the new schemes by solving various numerical and practical examples, demonstrating their superior efficiency in terms of computational cost, CPU time, and accuracy compared to existing methods.</p></div>","PeriodicalId":50227,"journal":{"name":"Journal of Complexity","volume":null,"pages":null},"PeriodicalIF":1.8,"publicationDate":"2024-09-11","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://www.sciencedirect.com/science/article/pii/S0885064X24000736/pdfft?md5=6dc221bf6c1e2ffc085c2b830768b4e4&pid=1-s2.0-S0885064X24000736-main.pdf","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"142240453","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
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