Journal of Complexity最新文献_第4页

On the complexity of p-order cone programs 论p阶锥规划的复杂性

IF 1.8 2区数学

Journal of Complexity Pub Date : 2025-12-01 Epub Date: 2025-07-29 DOI: 10.1016/j.jco.2025.101979

Víctor Blanco , Victor Magron , Miguel Martínez-Antón

引用次数: 0

Upper and lower error bounds for a compact fourth-order finite-difference scheme for the wave equation with nonsmooth data 非光滑波动方程紧致四阶有限差分格式的误差上限和下限

IF 1.8 2区数学

Journal of Complexity Pub Date : 2025-12-01 Epub Date: 2025-06-30 DOI: 10.1016/j.jco.2025.101973

A. Zlotnik

{"title":"Upper and lower error bounds for a compact fourth-order finite-difference scheme for the wave equation with nonsmooth data","authors":"A. Zlotnik","doi":"10.1016/j.jco.2025.101973","DOIUrl":"10.1016/j.jco.2025.101973","url":null,"abstract":"<div><div>A compact three-level fourth-order finite-difference scheme for solving the 1d wave equation is studied. New error bounds of the fractional order <span><math><mi>O</mi><mo>(</mo><msup><mrow><mi>h</mi></mrow><mrow><mn>4</mn><mo>(</mo><mi>λ</mi><mo>−</mo><mn>1</mn><mo>)</mo><mo>/</mo><mn>5</mn></mrow></msup><mo>)</mo></math></span> are proved in the mesh energy norm in terms of data, for two initial functions from the Sobolev and Nikolskii spaces with the smoothness orders <em>λ</em> and <span><math><mi>λ</mi><mo>−</mo><mn>1</mn></math></span> and the free term with a dominated mixed smoothness of order <span><math><mi>λ</mi><mo>−</mo><mn>1</mn></math></span>, for <span><math><mn>1</mn><mo>⩽</mo><mi>λ</mi><mo>⩽</mo><mn>6</mn></math></span>. The corresponding lower error bounds are proved as well to ensure the sharpness in order of the above error bounds with respect to each of the initial functions and the free term for any <em>λ</em>. Moreover, they demonstrate that the upper error bounds cannot be improved if the Lebesgue summability indices in the error norm are weakened down to 1 both in <em>x</em> and <em>t</em> and simultaneously the summability indices in the norms of data are strengthened up to ∞ both in <em>x</em> and <em>t</em>. Numerical experiments confirming the sharpness of the mentioned orders for half-integer <em>λ</em> and piecewise polynomial data have already been carried out previously.</div></div>","PeriodicalId":50227,"journal":{"name":"Journal of Complexity","volume":"91 ","pages":"Article 101973"},"PeriodicalIF":1.8,"publicationDate":"2025-12-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"144549672","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

Geo-indistinguishable location obfuscation with inference error bounds 具有推理误差界的地理不可区分位置混淆

IF 1.8 2区数学

Journal of Complexity Pub Date : 2025-12-01 Epub Date: 2025-06-11 DOI: 10.1016/j.jco.2025.101970

Shun Zhang , Benfei Duan , Zhili Chen , Hong Zhong

引用次数: 0

Skewness of a randomized quasi-Monte Carlo estimate 随机拟蒙特卡罗估计的偏度

IF 1.8 2区数学

Journal of Complexity Pub Date : 2025-10-01 Epub Date: 2025-05-05 DOI: 10.1016/j.jco.2025.101956

Zexin Pan, Art B. Owen

{"title":"Skewness of a randomized quasi-Monte Carlo estimate","authors":"Zexin Pan, Art B. Owen","doi":"10.1016/j.jco.2025.101956","DOIUrl":"10.1016/j.jco.2025.101956","url":null,"abstract":"<div><div>Some recent work on confidence intervals for randomized quasi-Monte Carlo (RQMC) sampling found a surprising result: ordinary Student's <em>t</em> 95% confidence intervals based on a modest number of replicates were seen to be very effective and even more reliable than some bootstrap <em>t</em> intervals that were expected to be best. One potential explanation is that those RQMC estimates have small skewness. In this paper we give conditions under which the skewness is <span><math><mi>O</mi><mo>(</mo><msup><mrow><mi>n</mi></mrow><mrow><mi>ϵ</mi></mrow></msup><mo>)</mo></math></span> for any <span><math><mi>ϵ</mi><mo>></mo><mn>0</mn></math></span>, so ‘almost <span><math><mi>O</mi><mo>(</mo><mn>1</mn><mo>)</mo></math></span>’. Under a random generator matrix model, we can improve this rate to <span><math><mi>O</mi><mo>(</mo><msup><mrow><mi>n</mi></mrow><mrow><mo>−</mo><mn>1</mn><mo>/</mo><mn>2</mn><mo>+</mo><mi>ϵ</mi></mrow></msup><mo>)</mo></math></span> with very high probability. We also improve some probabilistic bounds on the distribution of the quality parameter <em>t</em> for a digital net in a prime base under random sampling of generator matrices.</div></div>","PeriodicalId":50227,"journal":{"name":"Journal of Complexity","volume":"90 ","pages":"Article 101956"},"PeriodicalIF":1.8,"publicationDate":"2025-10-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"143908058","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 upper and lower bounds for pathwise approximation of scalar SDEs with reflection 带反射的标量SDEs路径逼近的上界和下界

IF 1.8 2区数学

Journal of Complexity Pub Date : 2025-10-01 Epub Date: 2025-05-16 DOI: 10.1016/j.jco.2025.101959

Mario Hefter , André Herzwurm , Klaus Ritter

引用次数: 0

Tractability results for integration in subspaces of the Wiener algebra 维纳代数子空间积分的可溯性结果

IF 1.8 2区数学

Journal of Complexity Pub Date : 2025-10-01 Epub Date: 2025-04-16 DOI: 10.1016/j.jco.2025.101948

Josef Dick , Takashi Goda , Kosuke Suzuki

引用次数: 0

Multilevel Picard approximations overcome the curse of dimensionality in the numerical approximation of general semilinear PDEs with gradient-dependent nonlinearities 多阶皮卡德近似克服了一般非线性梯度半线性偏微分方程数值逼近的维数问题

IF 1.8 2区数学

Journal of Complexity Pub Date : 2025-10-01 Epub Date: 2025-04-04 DOI: 10.1016/j.jco.2025.101946

Ariel Neufeld , Tuan Anh Nguyen , Sizhou Wu

{"title":"Multilevel Picard approximations overcome the curse of dimensionality in the numerical approximation of general semilinear PDEs with gradient-dependent nonlinearities","authors":"Ariel Neufeld , Tuan Anh Nguyen , Sizhou Wu","doi":"10.1016/j.jco.2025.101946","DOIUrl":"10.1016/j.jco.2025.101946","url":null,"abstract":"<div><div>Neufeld and Wu (2023) <span><span>[49]</span></span> developed a multilevel Picard (MLP) algorithm which can approximately solve <em>general</em> semilinear parabolic PDEs with gradient-dependent nonlinearities, allowing also for coefficient functions of the corresponding PDE to be non-constant. By introducing a particular stochastic fixed-point equation (SFPE) motivated by the Feynman-Kac representation and the Bismut-Elworthy-Li formula and identifying the first and second component of the unique fixed-point of the SFPE with the unique viscosity solution of the PDE and its gradient, they proved convergence of their algorithm. However, it remained an open question whether the proposed MLP schema in Neufeld and Wu (2023) <span><span>[49]</span></span> does not suffer from the curse of dimensionality. In this paper, we prove that the MLP algorithm in Neufeld and Wu (2023) <span><span>[49]</span></span> indeed can overcome the curse of dimensionality, i.e. that its computational complexity only grows polynomially in the dimension <span><math><mi>d</mi><mo>∈</mo><mi>N</mi></math></span> and the reciprocal of the accuracy <em>ε</em>, under some suitable assumptions on the nonlinear part of the corresponding PDE.</div></div>","PeriodicalId":50227,"journal":{"name":"Journal of Complexity","volume":"90 ","pages":"Article 101946"},"PeriodicalIF":1.8,"publicationDate":"2025-10-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"144070001","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

Average case tractability of multivariate approximation with Gevrey type kernels Gevrey型核多元逼近的平均情况可跟踪性

IF 1.8 2区数学

Journal of Complexity Pub Date : 2025-10-01 Epub Date: 2025-05-05 DOI: 10.1016/j.jco.2025.101957

Wanting Lu , Heping Wang

引用次数: 0

Bounds for the sampling discretization error and their applications to the universal sampling discretization 抽样离散误差的界限及其在通用抽样离散中的应用

IF 1.8 2区数学

Journal of Complexity Pub Date : 2025-10-01 Epub Date: 2025-05-05 DOI: 10.1016/j.jco.2025.101958

E.D. Kosov , V.N. Temlyakov

引用次数: 0

Takashi Goda is the winner of the 2025 Joseph F. Traub Prize for Achievement in Information-Based Complexity 后田隆史是 2025 年约瑟夫-特劳布信息复杂性成就奖（Joseph F. Traub Prize for Achievement in Information-Based Complexity）的获得者。