Journal of Complexity最新文献

英文中文

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 Q1 MATHEMATICS

Journal of Complexity

Pub Date : 2025-06-30 DOI: 10.1016/j.jco.2025.101973

A. Zlotnik

A compact three-level fourth-order finite-difference scheme for solving the 1d wave equation is studied. New error bounds of the fractional order

O (h^{4 (λ - 1) / 5})

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 λ and

λ - 1

and the free term with a dominated mixed smoothness of order

λ - 1

, for

1 ⩽ λ ⩽ 6

. 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 λ. 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 x and t and simultaneously the summability indices in the norms of data are strengthened up to ∞ both in x and t. Numerical experiments confirming the sharpness of the mentioned orders for half-integer λ and piecewise polynomial data have already been carried out previously.

研究了求解一维波动方程的紧凑三阶四阶有限差分格式。对于Sobolev和Nikolskii空间中光滑阶为λ和λ−1的两个初始函数，以及光滑阶为λ−1的自由项，在网格能量范数上用数据证明了分数阶O（h4(λ−1)/5）的新的误差界。并证明了相应的误差下界，以确保上述误差下界相对于每个初始函数和任意λ的自由项的顺序的清晰度。此外，他们还证明，如果误差范数中的Lebesgue可和性指标在x和t中都减弱到1，同时在x和t中数据范数中的可和性指标都增强到∞，则误差上限无法提高。之前已经进行了数值实验，证实了上述阶对半整数λ和分段多项式数据的锐性。

{"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":"2025-06-30","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

Convergence analysis of a regularized iterative scheme for solving nonlinear problems 求解非线性问题的正则迭代格式的收敛性分析

IF 1.8 2区数学 Q1 MATHEMATICS

Journal of Complexity

Pub Date : 2025-06-23 DOI: 10.1016/j.jco.2025.101972

M.P. Rajan, Niloopher Salam

Nonlinear inverse and ill-posed problems occur in many practical applications and the regularization techniques are employed to get a stable approximate solution for the same. Although many schemes are available in literature, iterative regularization techniques are the most commonly used approaches. One such important method is the Levenberg-Marquardt scheme. However, the scheme involves computation of the Fréchet derivative at every iterate which makes it tedious and the restrictive assumptions on it often difficult to verify for practical scenarios. In this paper, we propose a simplified Levenberg-Marquardt scheme that has two benefits. Firstly, computation of the Fréchet derivative is required only once at the initial point and secondly, the convergence and optimal convergence rate of the method is established with weaker assumptions as compared to the standard method. We also provide numerical examples to illustrate the theory and, results clearly illustrate the advantages of the proposed scheme over the standard method.

在实际应用中经常遇到非线性逆问题和不适定问题，本文采用正则化技术得到了这些问题的稳定近似解。虽然文献中有许多方案可用，但迭代正则化技术是最常用的方法。其中一个重要的方法是Levenberg-Marquardt格式。然而，该方案涉及到在每次迭代中计算fr切特导数，这使得它很繁琐，并且它的限制性假设通常难以在实际场景中验证。在本文中，我们提出了一个简化的Levenberg-Marquardt格式，它有两个好处。首先，在初始点只需要计算一次fr切特导数；其次，与标准方法相比，该方法的收敛性和最优收敛率的假设较弱。我们还提供了数值例子来说明理论，结果清楚地说明了所提出的方案相对于标准方法的优势。

引用次数: 0

Rademacher learning rates for iterated random functions 迭代随机函数的Rademacher学习率

IF 1.8 2区数学 Q1 MATHEMATICS

Journal of Complexity

Pub Date : 2025-06-19 DOI: 10.1016/j.jco.2025.101971

Nikola Sandrić

Most supervised learning methods assume training data is drawn from an i.i.d. sample. However, real-world problems often exhibit temporal dependence and strong correlations between marginals of the data-generating process, rendering the i.i.d. assumption unrealistic. Such cases naturally involve time-series processes and Markov chains. The learning rates typically obtained in these settings remain independent of the data distribution, potentially leading to restrictive hypothesis classes and suboptimal sample complexities. We consider training data generated by an iterated random function that need not be irreducible or aperiodic. Assuming the governing function is contractive in its first argument and subject to certain regularity conditions on the hypothesis class, we first establish uniform convergence for the sample error. We then prove learnability of approximate empirical risk minimization and derive its learning rate bound. Both bounds depend explicitly on the data distribution through the Rademacher complexities of the hypothesis class, thereby better capturing properties of the data-generating distribution.

大多数监督式学习方法都假设训练数据是从一个id样本中提取的。然而，现实世界的问题往往表现出时间依赖性和数据生成过程边缘之间的强相关性，使得i.i.d.假设不现实。这种情况自然涉及时间序列过程和马尔可夫链。在这些设置中通常获得的学习率与数据分布无关，可能导致限制性假设类和次优样本复杂性。我们考虑由迭代随机函数生成的训练数据不一定是不可约的或非周期的。假设控制函数在第一个参数上是收缩的，并且在假设类上满足一定的正则性条件，我们首先建立了样本误差的一致收敛性。然后证明了近似经验风险最小化的可学习性，并推导了其学习率界。这两个边界都通过假设类的Rademacher复杂性显式依赖于数据分布，从而更好地捕获数据生成分布的属性。

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 Q1 MATHEMATICS

Journal of Complexity

Pub Date : 2025-06-11 DOI: 10.1016/j.jco.2025.101970

Shun Zhang , Benfei Duan , Zhili Chen , Hong Zhong

Geo-indistinguishability and expected inference error are two complementary statistical notions for location privacy. The joint guarantee of differential privacy (indistinguishability) and distortion privacy (inference error) limits the information leakage. This paper analyzes the dynamic location obfuscation mechanism called PIVE by Yu, Liu and Pu (NDSS 2017), and shows that PIVE fails to offer either of the privacy guarantees on adaptive Protection Location Sets (PLSs) as claimed. Specifically, we demonstrate that different PLSs could intersect with one another due to the defined search algorithm, and different apriori locations in the same PLS could have different protection diameters which causes the problematic proof of local differential privacy for PIVE. Besides, the condition introduced in PIVE is confirmed to be not sufficient for bounding expected inference errors against Bayesian attacks. To address these issues, we introduce a relaxed definition of geo-indistinguishability, propose a couple of correction approaches, and analyze their satisfied privacy characteristics.

地理不可分辨性和预期推断误差是位置隐私的两个互补的统计概念。差分隐私（不可区分性）和失真隐私（推理错误）的联合保证限制了信息的泄露。本文分析了Yu， Liu和Pu （NDSS 2017）提出的动态位置混淆机制PIVE，并表明PIVE不能像声称的那样对自适应保护位置集（pls）提供任何一种隐私保证。具体来说，我们证明了由于定义的搜索算法，不同的PLS可能会彼此相交，并且同一PLS中的不同先验位置可能具有不同的保护直径，这导致PIVE的局部差分隐私证明存在问题。此外，还证实了PIVE中引入的条件不足以限定针对贝叶斯攻击的预期推理错误。为了解决这些问题，我们引入了一个宽松的地理不可分辨性定义，提出了几种校正方法，并分析了它们满足的隐私特征。

引用次数: 0

A sixth-order bi-parametric iterative method for nonlinear systems: Theory, stability and computational complexity 非线性系统的六阶双参数迭代法：理论、稳定性和计算复杂度

IF 1.8 2区数学 Q1 MATHEMATICS

Journal of Complexity

Pub Date : 2025-06-06 DOI: 10.1016/j.jco.2025.101960

G Thangkhenpau, Sunil Panday

In this paper, we propose a new bi-parametric three-step iterative method with sixth-order convergence for solving systems of nonlinear equations. The method is formulated using the composition technique, which we uniquely apply twice within a single method - an approach that, to our knowledge, is the first of its kind in the literature. This allows us to incorporate two free disposable parameters, offering flexibility with enhanced performance, stability and adaptability. The local convergence behaviour is rigorously analysed within the framework of Banach spaces, where we establish theoretical bounds for the convergence radius and demonstrate uniqueness conditions under Lipschitz-continuous Fréchet derivative assumptions. The theoretical outcomes are supported by numerical experiments. Lastly, we evaluate the method's efficiency by exploring its basins of attraction and applying it to systems of nonlinear equations and boundary value problems.

本文提出了求解非线性方程组的一种新的双参数六阶收敛三步迭代法。该方法是使用合成技术制定的，我们在一种方法中独特地应用了两次——据我们所知，这种方法在文献中是第一次。这允许我们合并两个自由的一次性参数，提供增强性能，稳定性和适应性的灵活性。在Banach空间框架内严格分析了其局部收敛性，建立了收敛半径的理论边界，并证明了在Lipschitz-continuous fr chet导数假设下的唯一性条件。理论结果得到数值实验的支持。最后，我们通过探索其吸引力盆地并将其应用于非线性方程组和边值问题来评估该方法的有效性。

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 Q1 MATHEMATICS

Journal of Complexity

Pub Date : 2025-05-16 DOI: 10.1016/j.jco.2025.101959

Mario Hefter , André Herzwurm , Klaus Ritter

For scalar SDEs with a one-sided reflection we study pathwise approximation, globally on a compact time interval or at a single time point. We consider algorithms based on sequential evaluations of the driving Brownian motion and establish upper and lower bounds for the minimal errors. Exploiting the relation to a reflected Ornstein-Uhlenbeck process, we also provide a new upper bound for a Cox-Ingersoll-Ross process.

对于具有单侧反射的标量SDEs，我们研究了在紧时间区间上的全局路径逼近和在单个时间点上的全局路径逼近。我们考虑基于驱动布朗运动的顺序评估的算法，并建立最小误差的上界和下界。利用与反射的Ornstein-Uhlenbeck过程的关系，我们还为Cox-Ingersoll-Ross过程提供了一个新的上界。

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 Q1 MATHEMATICS

Journal of Complexity

Pub Date : 2025-05-05 DOI: 10.1016/j.jco.2025.101956

Zexin Pan, Art B. Owen

Some recent work on confidence intervals for randomized quasi-Monte Carlo (RQMC) sampling found a surprising result: ordinary Student's t 95% confidence intervals based on a modest number of replicates were seen to be very effective and even more reliable than some bootstrap t 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

O (n^{ϵ})

for any

ϵ > 0

, so ‘almost

O (1)

’. Under a random generator matrix model, we can improve this rate to

O (n^{- 1 / 2 + ϵ})

with very high probability. We also improve some probabilistic bounds on the distribution of the quality parameter t for a digital net in a prime base under random sampling of generator matrices.

最近一些关于随机准蒙特卡罗（RQMC）抽样置信区间的研究发现了一个令人惊讶的结果：基于少量重复的普通学生的t 95%置信区间被认为是非常有效的，甚至比一些期望最好的bootstrap t区间更可靠。一种可能的解释是，RQMC的估计偏差很小。在本文中，我们给出了任意ϵ>；0的偏度为O（nλ）的条件，因此‘几乎为O(1) ’。在随机生成器矩阵模型下，我们可以以非常高的概率将该速率提高到O（n−1/2+ ε）。我们还改进了一个数字网络在质数基中质量参数t分布的一些概率界。

{"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":"2025-05-05","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

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 Q1 MATHEMATICS

Journal of Complexity

Pub Date : 2025-05-05 DOI: 10.1016/j.jco.2025.101957

Wanting Lu , Heping Wang

We consider multivariate approximation problems in the average case setting with a zero mean Gaussian measure whose covariance kernel is a periodic Gevrey kernel. We investigate various notions of algebraic tractability and exponential tractability, and obtain necessary and sufficient conditions in terms of the parameters of the problem.

研究了具有零均值高斯测度的多元逼近问题，高斯测度的协方差核为周期Gevrey核。我们研究了代数可跟踪性和指数可跟踪性的各种概念，并根据问题的参数得到了问题的充分必要条件。

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 Q1 MATHEMATICS

Journal of Complexity

Pub Date : 2025-05-05 DOI: 10.1016/j.jco.2025.101958

E.D. Kosov , V.N. Temlyakov

In the first part of the paper we study absolute error of sampling discretization of the integral

L_{p}

-norm for function classes of continuous functions. We use basic approaches from chaining technique to provide general upper bounds for the error of sampling discretization of the

L_{p}

-norm on a given function class in terms of entropy numbers in the uniform norm of this class. As an example we apply these general results to obtain new error bounds for sampling discretization of the

L_{p}

-norms on classes of multivariate functions with mixed smoothness. In the second part of the paper we apply our general bounds to study the problem of universal sampling discretization.

本文第一部分研究了连续函数类的积分lp范数抽样离散化的绝对误差。我们用链技术的基本方法给出了给定函数类上的lp -范数抽样离散误差的一般上界，即该类一致范数中的熵数。作为一个例子，我们应用这些一般结果得到了混合光滑多变量函数类的lp -范数抽样离散化的新误差界。在论文的第二部分，我们应用我们的一般界来研究普遍抽样离散化问题。

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 Q1 MATHEMATICS

Journal of Complexity

Pub Date : 2025-04-16 DOI: 10.1016/j.jco.2025.101948

Josef Dick , Takashi Goda , Kosuke Suzuki

In this paper, we present some new (in-)tractability results related to the integration problem in subspaces of the Wiener algebra over the d-dimensional unit cube. We show that intractability holds for multivariate integration in the standard Wiener algebra in the deterministic setting, in contrast to polynomial tractability in an unweighted subspace of the Wiener algebra recently shown by Goda (2023). Moreover, we prove that multivariate integration in the subspace of the Wiener algebra introduced by Goda is strongly polynomially tractable if we switch to the randomized setting, where we obtain a better ε-exponent than the one implied by the standard Monte Carlo method. We also identify subspaces in which multivariate integration in the deterministic setting are (strongly) polynomially tractable and we compare these results with the bound which can be obtained via Hoeffding's inequality.

在本文中，我们提出了与 d 维单位立方体上的维纳代数子空间中的积分问题有关的一些新（不）可操作性结果。我们证明，在确定性环境中，标准维纳代数中的多元积分问题是难以解决的，这与戈达（2023）最近证明的维纳代数非加权子空间中的多项式可计算性截然不同。此外，我们还证明，如果切换到随机设置，戈达引入的维纳代数子空间中的多变量积分具有很强的多项式可操作性，在随机设置中，我们得到的ε指数比标准蒙特卡罗方法隐含的指数更好。我们还确定了确定性设置中多元积分（强）多项式可控的子空间，并将这些结果与通过霍夫定不等式得到的约束进行了比较。

引用次数: 0

首页上一页

下一页尾页

类型

全部化学•材料生命科学医学物理工程技术环境•农林材料科学地球科学法学管理学化学环境科学与生态学计算机科学教育学经济学农林科学人文科学生物学数学物理与天体物理心理学综合性期刊其他工业工程理学历史学农学文学信息工程

数据库

全部 ACS Publications Elsevier ieeexplore Springer The Royal Society of Chemistry Wiley

期刊

Journal of Complexity

全部 Acc. Chem. Res. ACS Applied Bio Materials ACS Appl. Electron. Mater. ACS Appl. Energy Mater. ACS Appl. Mater. Interfaces ACS Appl. Nano Mater. ACS Appl. Polym. Mater. ACS BIOMATER-SCI ENG ACS Catal. ACS Cent. Sci. ACS Chem. Biol. ACS Chemical Health & Safety ACS Chem. Neurosci. ACS Comb. Sci. ACS Earth Space Chem. ACS Energy Lett. ACS Infect. Dis. ACS Macro Lett. ACS Mater. Lett. ACS Med. Chem. Lett. ACS Nano ACS Omega ACS Photonics ACS Sens. ACS Sustainable Chem. Eng. ACS Synth. Biol. Anal. Chem. BIOCHEMISTRY-US Bioconjugate Chem. BIOMACROMOLECULES Chem. Res. Toxicol. Chem. Rev. Chem. Mater. CRYST GROWTH DES ENERG FUEL Environ. Sci. Technol. Environ. Sci. Technol. Lett. Eur. J. Inorg. Chem. IND ENG CHEM RES Inorg. Chem. J. Agric. Food. Chem. J. Chem. Eng. Data J. Chem. Educ. J. Chem. Inf. Model. J. Chem. Theory Comput. J. Med. Chem. J. Nat. Prod. J PROTEOME RES J. Am. Chem. Soc. LANGMUIR MACROMOLECULES Mol. Pharmaceutics Nano Lett. Org. Lett. ORG PROCESS RES DEV ORGANOMETALLICS J. Org. Chem. J. Phys. Chem. J. Phys. Chem. A J. Phys. Chem. B J. Phys. Chem. C J. Phys. Chem. Lett. Analyst Anal. Methods Biomater. Sci. Catal. Sci. Technol. Chem. Commun. Chem. Soc. Rev. CHEM EDUC RES PRACT CRYSTENGCOMM Dalton Trans. Energy Environ. Sci. ENVIRON SCI-NANO ENVIRON SCI-PROC IMP ENVIRON SCI-WAT RES Faraday Discuss. Food Funct. Green Chem. Inorg. Chem. Front. Integr. Biol. J. Anal. At. Spectrom. J. Mater. Chem. A J. Mater. Chem. B J. Mater. Chem. C Lab Chip Mater. Chem. Front. Mater. Horiz. MEDCHEMCOMM Metallomics Mol. Biosyst. Mol. Syst. Des. Eng. Nanoscale Nanoscale Horiz. Nat. Prod. Rep. New J. Chem. Org. Biomol. Chem. Org. Chem. Front. PHOTOCH PHOTOBIO SCI PCCP Polym. Chem.

﹀