发布求助
文献互助 智能选刊 最新文献

Advances in Computational Mathematics最新文献

筛选
英文 中文
Estimates for coefficients in Jacobi series for functions with limited regularity by fractional calculus 用分数微积分估算有限正则函数的雅可比数列系数
IF 1.7 3区 数学
Advances in Computational Mathematics Pub Date : 2024-07-08 DOI: 10.1007/s10444-024-10159-y
Guidong Liu, Wenjie Liu, Beiping Duan
{"title":"Estimates for coefficients in Jacobi series for functions with limited regularity by fractional calculus","authors":"Guidong Liu,&nbsp;Wenjie Liu,&nbsp;Beiping Duan","doi":"10.1007/s10444-024-10159-y","DOIUrl":"10.1007/s10444-024-10159-y","url":null,"abstract":"<div><p>In this paper, optimal estimates on the decaying rates of Jacobi expansion coefficients are obtained by fractional calculus for functions with algebraic and logarithmic singularities. This is inspired by the fact that integer-order derivatives fail to deal with singularity of fractional-type, while fractional calculus can. To this end, we first introduce new fractional Sobolev spaces defined as the range of the <span>(L^p)</span>-space under the Riemann-Liouville fractional integral. The connection between these new spaces and classical fractional-order Sobolev spaces is then elucidated. Under this framework, the optimal decaying rate of Jacobi expansion coefficients is obtained, based on which the projection errors under different norms are given. This work is expected to introduce fractional calculus into traditional fields in approximation theory and to explore the possibility in solving classical problems by this ‘new’ tool.</p></div>","PeriodicalId":50869,"journal":{"name":"Advances in Computational Mathematics","volume":"50 4","pages":""},"PeriodicalIF":1.7,"publicationDate":"2024-07-08","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"141556906","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":3,"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
An adaptive time-stepping Fourier pseudo-spectral method for the Zakharov-Rubenchik equation 扎哈罗夫-鲁本奇克方程的自适应时间步进傅立叶伪谱方法
IF 1.7 3区 数学
Advances in Computational Mathematics Pub Date : 2024-07-03 DOI: 10.1007/s10444-024-10155-2
Bingquan Ji, Xuanxuan Zhou
{"title":"An adaptive time-stepping Fourier pseudo-spectral method for the Zakharov-Rubenchik equation","authors":"Bingquan Ji,&nbsp;Xuanxuan Zhou","doi":"10.1007/s10444-024-10155-2","DOIUrl":"10.1007/s10444-024-10155-2","url":null,"abstract":"<div><p>An adaptive time-stepping scheme is developed for the Zakharov-Rubenchik system to resolve the multiple time scales accurately and to improve the computational efficiency during long-time simulations. The Crank-Nicolson formula and the Fourier pseudo-spectral method are respectively utilized for the temporal and spatial approximations. The proposed numerical method is proved to preserve the mass and energy conservative laws in the discrete levels exactly so that the magnetic field, the density of mass, and the fluid speed are stable on a general class of nonuniform time meshes. With the aid of the priori estimates derived from the discrete invariance and the newly proved discrete Gronwall inequality on variable time grids, sharp convergence analysis of the fully discrete scheme is established rigorously. Error estimate shows that the suggested adaptive time-stepping method can attain the second-order accuracy in time and the spectral accuracy in space. Extensive numerical experiments coupled with an adaptive time-stepping algorithm are presented to show the effectiveness of our numerical method in capturing the multiple time scale evolution for various velocity cases during the interactions of solitons.</p></div>","PeriodicalId":50869,"journal":{"name":"Advances in Computational Mathematics","volume":"50 4","pages":""},"PeriodicalIF":1.7,"publicationDate":"2024-07-03","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://link.springer.com/content/pdf/10.1007/s10444-024-10155-2.pdf","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"141495975","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":3,"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
Further analysis of multilevel Stein variational gradient descent with an application to the Bayesian inference of glacier ice models 多层次斯泰因变分梯度下降法的进一步分析及其在冰川冰模型贝叶斯推断中的应用
IF 1.7 3区 数学
Advances in Computational Mathematics Pub Date : 2024-07-03 DOI: 10.1007/s10444-024-10153-4
Terrence Alsup, Tucker Hartland, Benjamin Peherstorfer, Noemi Petra
{"title":"Further analysis of multilevel Stein variational gradient descent with an application to the Bayesian inference of glacier ice models","authors":"Terrence Alsup,&nbsp;Tucker Hartland,&nbsp;Benjamin Peherstorfer,&nbsp;Noemi Petra","doi":"10.1007/s10444-024-10153-4","DOIUrl":"10.1007/s10444-024-10153-4","url":null,"abstract":"<div><p>Multilevel Stein variational gradient descent is a method for particle-based variational inference that leverages hierarchies of surrogate target distributions with varying costs and fidelity to computationally speed up inference. The contribution of this work is twofold. First, an extension of a previous cost complexity analysis is presented that applies even when the exponential convergence rate of single-level Stein variational gradient descent depends on iteration-varying parameters. Second, multilevel Stein variational gradient descent is applied to a large-scale Bayesian inverse problem of inferring discretized basal sliding coefficient fields of the Arolla glacier ice. The numerical experiments demonstrate that the multilevel version achieves orders of magnitude speedups compared to its single-level version.</p></div>","PeriodicalId":50869,"journal":{"name":"Advances in Computational Mathematics","volume":"50 4","pages":""},"PeriodicalIF":1.7,"publicationDate":"2024-07-03","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"141495999","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":3,"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 an accurate numerical integration for the triangular and tetrahedral spectral finite elements 论三角形和四面体谱有限元的精确数值积分
IF 1.7 3区 数学
Advances in Computational Mathematics Pub Date : 2024-07-03 DOI: 10.1007/s10444-024-10173-0
Ziqing Xie, Shangyou Zhang
{"title":"On an accurate numerical integration for the triangular and tetrahedral spectral finite elements","authors":"Ziqing Xie,&nbsp;Shangyou Zhang","doi":"10.1007/s10444-024-10173-0","DOIUrl":"10.1007/s10444-024-10173-0","url":null,"abstract":"<div><p>In the triangular/tetrahedral spectral finite elements, we apply a bilinear/trilinear transformation to map a reference square/cube to a triangle/tetrahedron, which consequently maps the <span>(varvec{Q_k})</span> polynomial space on the reference element to a finite element space of rational/algebraic functions on the triangle/tetrahedron. We prove that the resulting finite element space, even under this singular referencing mapping, can retain the property of optimal-order approximation. In addition, we prove that the standard Gauss-Legendre numerical integration would provide sufficient accuracy so that the finite element solutions converge at the optimal order. In particular, the finite element method, with singular mappings and numerical integration, preserves <span>(varvec{P_k})</span> polynomials. That is, the <span>(varvec{Q_k})</span> finite element solution is exact if the true solution is a <span>(varvec{P_k})</span> polynomial. Numerical tests are provided, verifying all theoretic findings.</p></div>","PeriodicalId":50869,"journal":{"name":"Advances in Computational Mathematics","volume":"50 4","pages":""},"PeriodicalIF":1.7,"publicationDate":"2024-07-03","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"141495868","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":3,"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 of projected subgradient method with sparse or low-rank constraints 具有稀疏或低阶约束条件的投影子梯度法的收敛性
IF 1.7 3区 数学
Advances in Computational Mathematics Pub Date : 2024-07-02 DOI: 10.1007/s10444-024-10163-2
Hang Xu, Song Li, Junhong Lin
{"title":"Convergence of projected subgradient method with sparse or low-rank constraints","authors":"Hang Xu,&nbsp;Song Li,&nbsp;Junhong Lin","doi":"10.1007/s10444-024-10163-2","DOIUrl":"10.1007/s10444-024-10163-2","url":null,"abstract":"<div><p>Many problems in data science can be treated as recovering structural signals from a set of linear measurements, sometimes perturbed by dense noise or sparse corruptions. In this paper, we develop a unified framework of considering a nonsmooth formulation with sparse or low-rank constraint for meeting the challenges of mixed noises—bounded noise and sparse noise. We show that the nonsmooth formulations of the problems can be well solved by the projected subgradient methods at a rapid rate when initialized at any points. Consequently, nonsmooth loss functions (<span>(ell _1)</span>-minimization programs) are naturally robust against sparse noise. Our framework simplifies and generalizes the existing analyses including compressed sensing, matrix sensing, quadratic sensing, and bilinear sensing. Motivated by recent work on the stochastic gradient method, we also give some experimentally and theoretically preliminary results about the projected stochastic subgradient method.</p></div>","PeriodicalId":50869,"journal":{"name":"Advances in Computational Mathematics","volume":"50 4","pages":""},"PeriodicalIF":1.7,"publicationDate":"2024-07-02","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"141489640","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":3,"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
Extrapolated regularization of nearly singular integrals on surfaces 曲面上近奇异积分的外推正则化
IF 1.7 3区 数学
Advances in Computational Mathematics Pub Date : 2024-07-01 DOI: 10.1007/s10444-024-10161-4
J. Thomas Beale, Svetlana Tlupova
{"title":"Extrapolated regularization of nearly singular integrals on surfaces","authors":"J. Thomas Beale,&nbsp;Svetlana Tlupova","doi":"10.1007/s10444-024-10161-4","DOIUrl":"10.1007/s10444-024-10161-4","url":null,"abstract":"<div><p>We present a method for computing nearly singular integrals that occur when single or double layer surface integrals, for harmonic potentials or Stokes flow, are evaluated at points nearby. Such values could be needed in solving an integral equation when one surface is close to another or to obtain values at grid points. We replace the singular kernel with a regularized version having a length parameter <span>(delta )</span> in order to control discretization error. Analysis near the singularity leads to an expression for the error due to regularization which has terms with unknown coefficients multiplying known quantities. By computing the integral with three choices of <span>(delta )</span>, we can solve for an extrapolated value that has regularization error reduced to <span>(O(delta ^5))</span>, uniformly for target points on or near the surface. In examples with <span>(delta /h)</span> constant and moderate resolution, we observe total error about <span>(O(h^5))</span> close to the surface. For convergence as <span>(h rightarrow 0)</span>, we can choose <span>(delta )</span> proportional to <span>(h^q)</span> with <span>(q &lt; 1)</span> to ensure the discretization error is dominated by the regularization error. With <span>(q = 4/5)</span>, we find errors about <span>(O(h^4))</span>. For harmonic potentials, we extend the approach to a version with <span>(O(delta ^7))</span> regularization; it typically has smaller errors, but the order of accuracy is less predictable.</p></div>","PeriodicalId":50869,"journal":{"name":"Advances in Computational Mathematics","volume":"50 4","pages":""},"PeriodicalIF":1.7,"publicationDate":"2024-07-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"141489637","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":3,"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
Stochastic modeling of stationary scalar Gaussian processes in continuous time from autocorrelation data 根据自相关数据建立连续时间内静止标量高斯过程的随机模型
IF 1.7 3区 数学
Advances in Computational Mathematics Pub Date : 2024-06-24 DOI: 10.1007/s10444-024-10150-7
Martin Hanke
{"title":"Stochastic modeling of stationary scalar Gaussian processes in continuous time from autocorrelation data","authors":"Martin Hanke","doi":"10.1007/s10444-024-10150-7","DOIUrl":"10.1007/s10444-024-10150-7","url":null,"abstract":"<div><p>We consider the problem of constructing a vector-valued linear Markov process in continuous time, such that its first coordinate is in good agreement with given samples of the scalar autocorrelation function of an otherwise unknown stationary Gaussian process. This problem has intimate connections to the computation of a passive reduced model of a deterministic time-invariant linear system from given output data in the time domain. We construct the stochastic model in two steps. First, we employ the AAA algorithm to determine a rational function which interpolates the <i>z</i>-transform of the discrete data on the unit circle and use this function to assign the poles of the transfer function of the reduced model. Second, we choose the associated residues as the minimizers of a linear inequality constrained least squares problem which ensures the positivity of the transfer function’s real part for large frequencies. We apply this method to compute extended Markov models for stochastic processes obtained from generalized Langevin dynamics in statistical physics. Numerical examples demonstrate that the algorithm succeeds in determining passive reduced models and that the associated Markov processes provide an excellent match of the given data.</p></div>","PeriodicalId":50869,"journal":{"name":"Advances in Computational Mathematics","volume":"50 4","pages":""},"PeriodicalIF":1.7,"publicationDate":"2024-06-24","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://link.springer.com/content/pdf/10.1007/s10444-024-10150-7.pdf","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"141444892","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":3,"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
On relaxed inertial projection and contraction algorithms for solving monotone inclusion problems 论解决单调包含问题的松弛惯性投影和收缩算法
IF 1.7 3区 数学
Advances in Computational Mathematics Pub Date : 2024-06-18 DOI: 10.1007/s10444-024-10156-1
Bing Tan, Xiaolong Qin
{"title":"On relaxed inertial projection and contraction algorithms for solving monotone inclusion problems","authors":"Bing Tan,&nbsp;Xiaolong Qin","doi":"10.1007/s10444-024-10156-1","DOIUrl":"10.1007/s10444-024-10156-1","url":null,"abstract":"<div><p>We present three novel algorithms based on the forward-backward splitting technique for the solution of monotone inclusion problems in real Hilbert spaces. The proposed algorithms work adaptively in the absence of the Lipschitz constant of the single-valued operator involved thanks to the fact that there is a non-monotonic step size criterion used. The weak and strong convergence and the <i>R</i>-linear convergence of the developed algorithms are investigated under some appropriate assumptions. Finally, our algorithms are put into practice to address the restoration problem in the signal and image fields, and they are compared to some pertinent algorithms in the literature.</p></div>","PeriodicalId":50869,"journal":{"name":"Advances in Computational Mathematics","volume":"50 4","pages":""},"PeriodicalIF":1.7,"publicationDate":"2024-06-18","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"141425406","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":3,"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
Numerical methods for forward fractional Feynman–Kac equation 前向分数费曼-卡克方程的数值方法
IF 1.7 3区 数学
Advances in Computational Mathematics Pub Date : 2024-06-10 DOI: 10.1007/s10444-024-10152-5
Daxin Nie, Jing Sun, Weihua Deng
{"title":"Numerical methods for forward fractional Feynman–Kac equation","authors":"Daxin Nie,&nbsp;Jing Sun,&nbsp;Weihua Deng","doi":"10.1007/s10444-024-10152-5","DOIUrl":"10.1007/s10444-024-10152-5","url":null,"abstract":"<div><p>Fractional Feynman–Kac equation governs the functional distribution of the trajectories of anomalous diffusion. The non-commutativity of the integral fractional Laplacian and time-space coupled fractional substantial derivative, i.e., <span>(mathcal {A}^{s}{}_{0}partial _{t}^{1-alpha ,x}ne {}_{0}partial _{t}^{1-alpha ,x}mathcal {A}^{s})</span>, brings about huge challenges on the regularity and spatial error estimates for the forward fractional Feynman–Kac equation. In this paper, we first use the corresponding resolvent estimate obtained by the bootstrapping arguments and the generalized Hölder-type inequalities in Sobolev space to build the regularity of the solution, and then the fully discrete scheme constructed by convolution quadrature and finite element methods is developed. Also, the complete error analyses in time and space directions are respectively presented, which are consistent with the provided numerical experiments.</p></div>","PeriodicalId":50869,"journal":{"name":"Advances in Computational Mathematics","volume":"50 3","pages":""},"PeriodicalIF":1.7,"publicationDate":"2024-06-10","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"141299089","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":3,"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
An efficient rotational pressure-correction schemes for 2D/3D closed-loop geothermal system 二维/三维闭环地热系统的高效旋转压力校正方案
IF 1.7 3区 数学
Advances in Computational Mathematics Pub Date : 2024-06-10 DOI: 10.1007/s10444-024-10154-3
Jian Li, Jiawei Gao, Yi Qin
{"title":"An efficient rotational pressure-correction schemes for 2D/3D closed-loop geothermal system","authors":"Jian Li,&nbsp;Jiawei Gao,&nbsp;Yi Qin","doi":"10.1007/s10444-024-10154-3","DOIUrl":"10.1007/s10444-024-10154-3","url":null,"abstract":"<div><p>In this paper, the rotational pressure-correction schemes for the closed-loop geothermal system are developed and analyzed. The primary benefit of this projection method is to replace the incompressible condition. The system is considered consisting of two distinct regions, with the free flow region governed by the Navier–Stokes equations and the porous media region governed by Darcy’s law. At the same time, the heat equations are coupled with the flow equations to describe the heat transfer in both regions. In the closed-loop geothermal system, the rotational pressure-correction schemes are used for the Navier–Stokes equations in the free flow region, and the direct decoupled scheme is used for the other equations. Besides, the stability of the proposed methods is proved. Finally, the high efficiency and applicability of the decoupled scheme are verified by 2D/3D numerical experiments.</p></div>","PeriodicalId":50869,"journal":{"name":"Advances in Computational Mathematics","volume":"50 3","pages":""},"PeriodicalIF":1.7,"publicationDate":"2024-06-10","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"141299063","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":3,"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
首页 上一页 下一页 尾页
0
×
引用
GB/T 7714-2015
复制
MLA
复制
APA
复制
导出至
BibTeX EndNote RefMan NoteFirst NoteExpress
×
提示
您的信息不完整，为了账户安全，请先补充。
现在去补充
×
提示
您因"违规操作"
具体请查看互助需知
我知道了
×
提示
现在去查看 取消
×
提示
确定
请完成安全验证×
相关产品
×
本文献相关产品
联系我们：info@booksci.cn Book学术提供免费学术资源搜索服务，方便国内外学者检索中英文文献。致力于提供最便捷和优质的服务体验。 Copyright © 2023 布克学术 All rights reserved.
京ICP备2023020795号-1
ghs 京公网安备 11010802042870号
Book学术文献互助
Book学术文献互助群
群 号：481959085
Book学术官方微信