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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 : 2025-04-01 Epub 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":"2025-04-01","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
A revisit on Nesterov acceleration for linear ill-posed problems 线性不适定问题的Nesterov加速问题的再探讨
IF 1.8 2区 数学
Journal of Complexity Pub Date : 2025-04-01 Epub Date: 2024-12-04 DOI: 10.1016/j.jco.2024.101920
Duo Liu , Qin Huang , Qinian Jin
{"title":"A revisit on Nesterov acceleration for linear ill-posed problems","authors":"Duo Liu ,&nbsp;Qin Huang ,&nbsp;Qinian Jin","doi":"10.1016/j.jco.2024.101920","DOIUrl":"10.1016/j.jco.2024.101920","url":null,"abstract":"<div><div>In recent years, Nesterov acceleration has been introduced to enhance the efficiency of Landweber iteration for solving ill-posed problems. For linear ill-posed problems in Hilbert spaces, Nesterov acceleration has been analyzed with a discrepancy principle proposed to terminate the iterations. However, the existing approach requires computing residuals along two distinct iterative sequences, resulting in increased computational costs. In this paper, we propose an alternative discrepancy principle for Nesterov acceleration that eliminates the need to compute the residuals for one of the iterative sequences, thereby reducing computational time by approximately one-third per iteration. We provide a convergence analysis of the proposed method, establishing both its convergence and convergence rates. The effectiveness of our approach is demonstrated through numerical simulations.</div></div>","PeriodicalId":50227,"journal":{"name":"Journal of Complexity","volume":"87 ","pages":"Article 101920"},"PeriodicalIF":1.8,"publicationDate":"2025-04-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"143180615","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
A procedure for increasing the convergence order of iterative methods from p to 5p for solving nonlinear system 求解非线性系统的迭代法收敛阶由p提高到5p的程序
IF 1.8 2区 数学
Journal of Complexity Pub Date : 2025-04-01 Epub Date: 2024-12-06 DOI: 10.1016/j.jco.2024.101921
Santhosh George , Muniyasamy M , Manjusree Gopal , Chandhini G , Ioannis K. Argyros
{"title":"A procedure for increasing the convergence order of iterative methods from p to 5p for solving nonlinear system","authors":"Santhosh George ,&nbsp;Muniyasamy M ,&nbsp;Manjusree Gopal ,&nbsp;Chandhini G ,&nbsp;Ioannis K. Argyros","doi":"10.1016/j.jco.2024.101921","DOIUrl":"10.1016/j.jco.2024.101921","url":null,"abstract":"<div><div>In this paper, we propose a procedure to obtain an iterative method that increases its convergence order from <em>p</em> to 5<em>p</em> for solving nonlinear systems. Our analysis is given in more general Banach space settings and uses assumptions on the derivative of the involved operator only up to order <span><math><mi>max</mi><mo>⁡</mo><mo>{</mo><mi>k</mi><mo>,</mo><mn>2</mn><mo>}</mo></math></span>. Here, <em>k</em> is the order of the highest derivative used in the convergence analysis of the iterative method with convergence order <em>p</em>. A particular case of our analysis includes an existing fifth-order method and improves its applicability to more problems than the problems covered by the method's analysis in earlier study.</div></div>","PeriodicalId":50227,"journal":{"name":"Journal of Complexity","volume":"87 ","pages":"Article 101921"},"PeriodicalIF":1.8,"publicationDate":"2025-04-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"143180612","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 interpolation of multivariate polynomials with sparse exponents 具有稀疏指数的多元多项式的快速插值
IF 1.8 2区 数学
Journal of Complexity Pub Date : 2025-04-01 Epub Date: 2024-12-16 DOI: 10.1016/j.jco.2024.101922
Joris van der Hoeven, Grégoire Lecerf
{"title":"Fast interpolation of multivariate polynomials with sparse exponents","authors":"Joris van der Hoeven,&nbsp;Grégoire Lecerf","doi":"10.1016/j.jco.2024.101922","DOIUrl":"10.1016/j.jco.2024.101922","url":null,"abstract":"<div><div>Consider a sparse multivariate polynomial <em>f</em> with integer coefficients. Assume that <em>f</em> is represented as a “modular black box polynomial”, e.g. via an algorithm to evaluate <em>f</em> at arbitrary integer points, modulo arbitrary positive integers. The problem of sparse interpolation is to recover <em>f</em> in its usual sparse representation, as a sum of coefficients times monomials. For the first time we present a quasi-optimal algorithm for this task in term of the product of the number of terms of <em>f</em> by the maximum of the bit-size of the terms of <em>f</em>.</div></div>","PeriodicalId":50227,"journal":{"name":"Journal of Complexity","volume":"87 ","pages":"Article 101922"},"PeriodicalIF":1.8,"publicationDate":"2025-04-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"143180614","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 : 2025-04-01 Epub 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":"2025-04-01","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 : 2025-02-01 Epub 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,&nbsp;Mario Ullrich,&nbsp;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":"86 ","pages":"Article 101905"},"PeriodicalIF":1.8,"publicationDate":"2025-02-01","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
On the approximation of vector-valued functions by volume sampling 关于用体积采样法逼近矢量值函数
IF 1.8 2区 数学
Journal of Complexity Pub Date : 2025-02-01 Epub Date: 2024-07-31 DOI: 10.1016/j.jco.2024.101887
Daniel Kressner , Tingting Ni , André Uschmajew
{"title":"On the approximation of vector-valued functions by volume sampling","authors":"Daniel Kressner ,&nbsp;Tingting Ni ,&nbsp;André Uschmajew","doi":"10.1016/j.jco.2024.101887","DOIUrl":"10.1016/j.jco.2024.101887","url":null,"abstract":"<div><p>Given a Hilbert space <span><math><mi>H</mi></math></span> and a finite measure space Ω, the approximation of a vector-valued function <span><math><mi>f</mi><mo>:</mo><mi>Ω</mi><mo>→</mo><mi>H</mi></math></span> by a <em>k</em>-dimensional subspace <span><math><mi>U</mi><mo>⊂</mo><mi>H</mi></math></span> plays an important role in dimension reduction techniques, such as reduced basis methods for solving parameter-dependent partial differential equations. For functions in the Lebesgue–Bochner space <span><math><msup><mrow><mi>L</mi></mrow><mrow><mn>2</mn></mrow></msup><mo>(</mo><mi>Ω</mi><mo>;</mo><mi>H</mi><mo>)</mo></math></span>, the best possible subspace approximation error <span><math><msubsup><mrow><mi>d</mi></mrow><mrow><mi>k</mi></mrow><mrow><mo>(</mo><mn>2</mn><mo>)</mo></mrow></msubsup></math></span> is characterized by the singular values of <em>f</em>. However, for practical reasons, <span><math><mi>U</mi></math></span> is often restricted to be spanned by point samples of <em>f</em>. We show that this restriction only has a mild impact on the attainable error; there always exist <em>k</em> samples such that the resulting error is not larger than <span><math><msqrt><mrow><mi>k</mi><mo>+</mo><mn>1</mn></mrow></msqrt><mo>⋅</mo><msubsup><mrow><mi>d</mi></mrow><mrow><mi>k</mi></mrow><mrow><mo>(</mo><mn>2</mn><mo>)</mo></mrow></msubsup></math></span>. Our work extends existing results by Binev et al. (2011) <span><span>[3]</span></span> on approximation in supremum norm and by Deshpande et al. (2006) <span><span>[8]</span></span> on column subset selection for matrices.</p></div>","PeriodicalId":50227,"journal":{"name":"Journal of Complexity","volume":"86 ","pages":"Article 101887"},"PeriodicalIF":1.8,"publicationDate":"2025-02-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://www.sciencedirect.com/science/article/pii/S0885064X24000645/pdfft?md5=810287a810b23405b1bc8161d82ba70e&pid=1-s2.0-S0885064X24000645-main.pdf","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"141935983","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
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 : 2025-02-01 Epub 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":"86 ","pages":"Article 101899"},"PeriodicalIF":1.8,"publicationDate":"2025-02-01","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 : 2025-02-01 Epub 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":"86 ","pages":"Article 101898"},"PeriodicalIF":1.8,"publicationDate":"2025-02-01","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
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 : 2025-02-01 Epub 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":"2025-02-01","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
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