Advances in Computational Mathematics最新文献_第3页

Energy function approximations for differential algebraic polynomial systems of Stokes-type stokes型微分代数多项式系统的能量函数逼近

IF 2.6 3区数学

Advances in Computational Mathematics Pub Date : 2026-09-07 DOI: 10.1007/s10444-026-10351-2

Hamza Adjerid, Jeff Borggaard

{"title":"Energy function approximations for differential algebraic polynomial systems of Stokes-type","authors":"Hamza Adjerid, Jeff Borggaard","doi":"10.1007/s10444-026-10351-2","DOIUrl":"10.1007/s10444-026-10351-2","url":null,"abstract":"<div><p>Energy functions are generalizations of controllability and observability Gramians to nonlinear systems and as such find applications in both nonlinear balanced truncation and feedback control. These energy functions are solutions to the Hamilton-Jacobi-Bellman (HJB) equations—partial differential equations defined over spatial dimensions determined by the number of state variables in the nonlinear system. Thus, they cannot be resolved with local basis functions, even for problems of modest dimension. In this paper, we extend recent results that utilize Kronecker products to generate polynomial approximations to HJB equations. Specifically, we consider the addition of linear constraints that exhibit a Stokes-type differential-algebraic equation (DAE) structure. This extension leverages the so-called <i>strangeness framework</i> for DAEs to create separate sets of algebraic and differential variables with differential equations that only involve the differential variables and algebraic equations that relate them both. At this point, the existing polynomial approximations using Kronecker products can be applied to find approximations to the energy functions. This approach is demonstrated on two polynomial feedback control problems. While the standard transformation destroys the sparsity in the original system, we present a formulation that preserves the original sparsity structure.</p></div>","PeriodicalId":50869,"journal":{"name":"Advances in Computational Mathematics","volume":"52 5","pages":""},"PeriodicalIF":2.6,"publicationDate":"2026-09-07","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://link.springer.com/content/pdf/10.1007/s10444-026-10351-2.pdf","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"148926726","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

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 2.6 3区数学

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

Ljiljana Cvetković

{"title":"Partition-based bounds for the norm of the inverse of monotone matrices and totally non-negative matrices","authors":"Ljiljana Cvetković","doi":"10.1007/s10444-026-10355-y","DOIUrl":"10.1007/s10444-026-10355-y","url":null,"abstract":"<div><p>This paper introduces a novel approach for estimating the infinity norm of the inverse of monotone (inverse-positive) matrices and totally non-negative matrices. The proposed method is based on a partition of the index set into two complementary subsets. By considering partial row sums associated with this partition, the problem is reduced to the analysis of an auxiliary 2<span>(times )</span>2 matrix that captures the aggregated interaction between the subsets. The main result shows that if the constructed 2<span>(times )</span>2 matrix preserves the monotonicity property, then an explicit upper bound for the infinity norm of the inverse can be derived. This reduction principle enables greater flexibility in applications, as the partition can be adapted to the structure of the matrix, such as sparsity or block patterns. Furthermore, the new bounds generalize existing row-sum-based estimates, which can be viewed as the limit case corresponding to a trivial partition. The approach is extended to totally non-negative matrices via a standard sign transformation, preserving the structure of the obtained bounds. Numerical examples demonstrate that the proposed estimates can be significantly sharper than classical bounds, highlighting their practical relevance in stability analysis and numerical linear algebra.</p></div>","PeriodicalId":50869,"journal":{"name":"Advances in Computational Mathematics","volume":"52 5","pages":""},"PeriodicalIF":2.6,"publicationDate":"2026-09-02","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"148883439","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 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 2.6 3区数学

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

Qing Xia

{"title":"An unfitted boundary algebraic equation method based on difference potentials and lattice Green’s function in 3D","authors":"Qing Xia","doi":"10.1007/s10444-026-10346-z","DOIUrl":"10.1007/s10444-026-10346-z","url":null,"abstract":"<div><p>This work presents a novel unfitted boundary algebraic equation method for solving three-dimensional elliptic partial differential equations in complex geometries. The developed method can be regarded as a finite difference version of the boundary integral method. We demonstrate that replacing finite auxiliary domains with free-space lattice Green’s functions streamlines the computation of difference potentials, enabling matrix-free implementations and significant reductions of computational cost. We establish theoretical foundations by proving the equivalence of densities obtained from finite and infinite auxiliary domains when the grids align, and by showing the equivalence between direct formulations in the difference potentials framework and indirect single- and double-layer formulations. Spectral analysis of the resulting boundary systems reveals that the discrete single-layer matrix has a condition number growing linearly with boundary size, while the discrete double-layer matrix remains uniformly bounded. The method is validated through matrix-free numerical experiments on Poisson’s and modified Helmholtz equations in 3D implicitly defined geometries, including ellipsoids, bumped spheres, and tori, demonstrating optimal second-order convergence rates and computational efficiency. Numerical results also reveal that the double-layer formulation requires fewer GMRES iterations for smooth geometries, compared to the single-layer formulations. This framework naturally extends to unbounded domains and provides a foundation for applications to more complex systems like Helmholtz and Stokes equations.</p></div>","PeriodicalId":50869,"journal":{"name":"Advances in Computational Mathematics","volume":"52 5","pages":""},"PeriodicalIF":2.6,"publicationDate":"2026-09-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"148883440","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

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 2.6 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

{"title":"Diagonalization-based algorithms for all-at-once systems arising from linear delay differential equations","authors":"Qing-Yang Si, Yu-Hong Ran, Jun-Gang Wang, Zong-Ze Yang","doi":"10.1007/s10444-026-10354-z","DOIUrl":"10.1007/s10444-026-10354-z","url":null,"abstract":"<div><p>This paper develops diagonalization-based algorithms for all-at-once linear systems arising from linear delay differential equations. The fully discrete all-at-once systems are approximated by their <span>(alpha )</span>-circulant counterparts and then decoupled in the frequency domain, providing the basis for the proposed solvers. First, we propose an <span>(alpha )</span>-circulant preconditioner for GMRES solvers. By employing a generalized Bendixson theorem, we derive a spectral enclosure for the preconditioned operator and characterize how the eigenvalue clustering around unity depends on <span>(alpha )</span>. Second, we develop a parallel low-rank correction method which decomposes the correction equation into a collection of independent rank-one generalized Sylvester-type matrix equations. These subproblems are solved by a two-sided Krylov subspace projection method. We analyze the low-rank structure of the subproblem solutions and characterize the polynomial nature of the underlying approximation spaces. The theoretical speedup models illustrate the algorithmic parallel potential of the two methods. Numerical experiments validate the robust convergence and computational effectiveness of the proposed methods.</p></div>","PeriodicalId":50869,"journal":{"name":"Advances in Computational Mathematics","volume":"52 5","pages":""},"PeriodicalIF":2.6,"publicationDate":"2026-09-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"148883441","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

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