Advances in Computational Mathematics最新文献

Partition-based bounds for the norm of the inverse of monotone matrices and totally non-negative matrices 单调矩阵和全非负矩阵逆模的分划界

IF 1.7 3区数学

Advances in Computational Mathematics Pub Date : 2026-09-02 DOI: 10.1007/s10444-026-10355-y

Ljiljana Cvetković

引用次数: 0

An unfitted boundary algebraic equation method based on difference potentials and lattice Green’s function in 3D 基于差分势和格格林函数的三维非拟合边界代数方程方法

IF 1.7 3区数学

Advances in Computational Mathematics Pub Date : 2026-09-01 DOI: 10.1007/s10444-026-10346-z

Qing Xia

引用次数: 0

Diagonalization-based algorithms for all-at-once systems arising from linear delay differential equations 线性时滞微分方程瞬时系统的对角算法

IF 1.7 3区数学

Advances in Computational Mathematics Pub Date : 2026-09-01 DOI: 10.1007/s10444-026-10354-z

Qing-Yang Si, Yu-Hong Ran, Jun-Gang Wang, Zong-Ze Yang

引用次数: 0

Eigenvalue bounds of saddle point matrix from mixed-cell-height integrated circuit legalization problem 混合单元高度集成电路合法化问题鞍点矩阵的特征值界

IF 2.6 3区数学

Advances in Computational Mathematics Pub Date : 2026-08-26 DOI: 10.1007/s10444-026-10352-1

Yang Cao, Lu-Xin Wang, Qin-Qin Shen, Chen-Can Zhou

{"title":"Eigenvalue bounds of saddle point matrix from mixed-cell-height integrated circuit legalization problem","authors":"Yang Cao, Lu-Xin Wang, Qin-Qin Shen, Chen-Can Zhou","doi":"10.1007/s10444-026-10352-1","DOIUrl":"10.1007/s10444-026-10352-1","url":null,"abstract":"<div><p>Reformulating the mixed-cell-height integrated circuit legalization problem into a linear complementarity problem (LCP) has been proven to be a useful tool in very large-scale integrated circuit placement design. An important characteristic of such LCP is that the system matrix is a typical saddle point matrix with the (1,1) leading block being a summation of the identity matrix and a symmetric positive-semidefinite matrix. In this paper, the eigenvalue bounds of this special saddle point matrix are studied in detail. More specifically, for the real eigenvalues, the lower bound is a value larger than <span>(varvec{0})</span> and less than <span>(varvec{1})</span>, while the upper bound is less than <span>(varvec{1+4mu })</span>, where <span>(varvec{mu })</span> is the Lagrange multiplier. For the complex eigenvalues, the real parts fall within the left-closed and right-open range of <span>(varvec{frac{1}{2}})</span> to 2, while the upper bound of the modulus of the imaginary parts is less than <span>(varvec{frac{1}{2}sqrt{15}})</span>. In particular, for the case where there are only single-row-height cells, some refined bounds are derived. Finally, these theoretical findings are verified through five numerical examples.</p></div>","PeriodicalId":50869,"journal":{"name":"Advances in Computational Mathematics","volume":"52 5","pages":""},"PeriodicalIF":2.6,"publicationDate":"2026-08-26","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"148837668","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

Second-order AAA algorithms for structured data-driven modeling 结构化数据驱动建模的二阶AAA算法

IF 2.6 3区数学

Advances in Computational Mathematics Pub Date : 2026-08-26 DOI: 10.1007/s10444-026-10347-y

Michael S. Ackermann, Ion Victor Gosea, Serkan Gugercin, Steffen W. R. Werner

{"title":"Second-order AAA algorithms for structured data-driven modeling","authors":"Michael S. Ackermann, Ion Victor Gosea, Serkan Gugercin, Steffen W. R. Werner","doi":"10.1007/s10444-026-10347-y","DOIUrl":"10.1007/s10444-026-10347-y","url":null,"abstract":"<div><p>The data-driven modeling of dynamical systems has become an essential tool for the construction of accurate computational models from real-world data. In this process, the inherent differential structures underlying the considered physical phenomena are often neglected making the reinterpretation of the learned models in a physically meaningful sense very challenging. In this work, we present three data-driven modeling approaches for the construction of dynamical systems with second-order differential structure directly from frequency domain data. Based on the second-order structured barycentric form, we extend the well-known Adaptive Antoulas-Anderson algorithm to the case of second-order systems. Depending on the available computational resources, we propose variations of the proposed method that prioritize either higher computation speed or greater modeling accuracy, and we present a theoretical analysis for the expected accuracy and performance of the proposed methods. Three numerical examples demonstrate the effectiveness of our new structured approaches in comparison to classical unstructured data-driven modeling.</p></div>","PeriodicalId":50869,"journal":{"name":"Advances in Computational Mathematics","volume":"52 5","pages":""},"PeriodicalIF":2.6,"publicationDate":"2026-08-26","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://link.springer.com/content/pdf/10.1007/s10444-026-10347-y.pdf","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"148837666","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

A novel penalty-based least-squares discontinuous Galerkin (LS-DG) method for time-dependent Stokes equations 基于惩罚的最小二乘不连续伽辽金（LS-DG）方法求解时变Stokes方程

IF 2.6 3区数学

Advances in Computational Mathematics Pub Date : 2026-08-26 DOI: 10.1007/s10444-026-10349-w

Guang-an Zou, Kejia Pan, Xiaofeng Yang

{"title":"A novel penalty-based least-squares discontinuous Galerkin (LS-DG) method for time-dependent Stokes equations","authors":"Guang-an Zou, Kejia Pan, Xiaofeng Yang","doi":"10.1007/s10444-026-10349-w","DOIUrl":"10.1007/s10444-026-10349-w","url":null,"abstract":"<div><p>In this paper, a new penalty-based least-squares discontinuous Galerkin (LS-DG) framework is proposed and analyzed for the time-dependent Stokes system. A key feature of the scheme is the use of a penalty method to address the incompressibility constraint, along with the introduction of an artificial average perturbation term in the weighted least-squares functional. This approach offers three distinct advantages: first, it facilitates the proof of coercivity of the functional, ensuring the unique solvability of the method; second, it guarantees the unconditional stability of the kinetic energy at the discrete level; and third, it integrates the strengths of both the discontinuous Galerkin and least-squares methods, naturally providing a built-in residual indicator for the adaptive procedure. We rigorously establish the well-posedness and derive optimal error estimates for the proposed scheme. Finally, the accuracy, energy stability, and high efficiency of the method are demonstrated through several numerical examples, which show that it outperforms the classical DG method in terms of computational efficiency.</p></div>","PeriodicalId":50869,"journal":{"name":"Advances in Computational Mathematics","volume":"52 5","pages":""},"PeriodicalIF":2.6,"publicationDate":"2026-08-26","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://link.springer.com/content/pdf/10.1007/s10444-026-10349-w.pdf","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"148837665","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

How to induce regularization in linear models: a guide to reparametrizing gradient flow 如何在线性模型中引入正则化：梯度流的再参数化指南

IF 2.6 3区数学

Advances in Computational Mathematics Pub Date : 2026-08-26 DOI: 10.1007/s10444-026-10350-3

Hung-Hsu Chou, Johannes Maly, Dominik Stöger

引用次数: 0

A class of improved randomized Gauss-Seidel methods based on the leverage scores for the parameter estimation of TAR model 一类改进的基于杠杆分数的随机化Gauss-Seidel方法用于TAR模型的参数估计

IF 2.6 3区数学

Advances in Computational Mathematics Pub Date : 2026-08-26 DOI: 10.1007/s10444-026-10353-0

Zhang-Yang Xu, Ju-Li Zhang

引用次数: 0

High order regularization of nearly singular surface integrals 近奇异曲面积分的高阶正则化

IF 2.6 3区数学

Advances in Computational Mathematics Pub Date : 2026-08-25 DOI: 10.1007/s10444-026-10344-1

J. Thomas Beale, Svetlana Tlupova

{"title":"High order regularization of nearly singular surface integrals","authors":"J. Thomas Beale, Svetlana Tlupova","doi":"10.1007/s10444-026-10344-1","DOIUrl":"10.1007/s10444-026-10344-1","url":null,"abstract":"<div><p>Solutions of partial differential equations can often be written as surface integrals having a kernel related to a singular fundamental solution. Special methods are needed to evaluate the integral accurately at points on or near the surface. Here, we derive formulas to regularize the integrals with high accuracy, using analysis from [6], so that a standard quadrature can be used without special care near the singularity. We treat single or double layer integrals for harmonic functions or for Stokes flow. The nearly singular case, evaluation at points close to the surface, can be needed when surfaces are close to each other, or to find values at grid points near a surface. We derive formulas for regularized kernels with error <span>(O(delta ^p))</span> where <span>(delta )</span> is the smoothing radius and <span>(p = 3)</span>, 5, 7. With spacing <i>h</i> in the quadrature, we choose <span>(delta )</span> proportional to <span>(h^q)</span> with <span>(q<1)</span> so that the discretization error is controlled as <span>(h rightarrow 0)</span>. We see the predicted order of convergence <span>(O(h^{pq}))</span> in various examples. Values at all grid points can be obtained from those near the surface in an efficient manner suggested in [20]. With this technique, we obtain high-order accurate grid values for a harmonic function determined by interfacial conditions and for the pressure and velocity in Stokes flow around a translating spheroid.</p></div>","PeriodicalId":50869,"journal":{"name":"Advances in Computational Mathematics","volume":"52 5","pages":""},"PeriodicalIF":2.6,"publicationDate":"2026-08-25","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"148837688","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

Block-randomized stochastic methods for tensor ring decomposition 张量环分解的块随机方法

IF 2.6 3区数学

Advances in Computational Mathematics Pub Date : 2026-08-24 DOI: 10.1007/s10444-026-10333-4

Yajie Yu, Hanyu Li, Jingchun Zhou

引用次数: 0