arXiv - CS - Numerical Analysis最新文献_第6页

Efficient solution of sequences of parametrized Lyapunov equations with applications 参数化 Lyapunov 方程序列的高效解法及其应用

arXiv - CS - Numerical Analysis Pub Date : 2023-12-13 DOI: arxiv-2312.08201

Davide Palitta, Zoran Tomljanović, Ivica Nakić, Jens Saak

{"title":"Efficient solution of sequences of parametrized Lyapunov equations with applications","authors":"Davide Palitta, Zoran Tomljanović, Ivica Nakić, Jens Saak","doi":"arxiv-2312.08201","DOIUrl":"https://doi.org/arxiv-2312.08201","url":null,"abstract":"Sequences of parametrized Lyapunov equations can be encountered in many\u0000application settings. Moreover, solutions of such equations are often\u0000intermediate steps of an overall procedure whose main goal is the computation\u0000of quantities of the form $f(X)$ where $X$ denotes the solution of a Lyapunov\u0000equation. We are interested in addressing problems where the parameter\u0000dependency of the coefficient matrix is encoded as a low-rank modification to a\u0000emph{seed}, fixed matrix. We propose two novel numerical procedures that fully\u0000exploit such a common structure. The first one builds upon recycling Krylov\u0000techniques, and it is well-suited for small dimensional problems as it makes\u0000use of dense numerical linear algebra tools. The second algorithm can instead\u0000address large-scale problems by relying on state-of-the-art projection\u0000techniques based on the extended Krylov subspace. We test the new algorithms on\u0000several problems arising in the study of damped vibrational systems and the\u0000analyses of output synchronization problems for multi-agent systems. Our\u0000results show that the algorithms we propose are superior to state-of-the-art\u0000techniques as they are able to remarkably speed up the computation of accurate\u0000solutions.","PeriodicalId":501061,"journal":{"name":"arXiv - CS - Numerical Analysis","volume":"51 1","pages":""},"PeriodicalIF":0.0,"publicationDate":"2023-12-13","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"138630442","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","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 Hermite approximations for analytic functions 解析函数赫米特近似的收敛性分析

arXiv - CS - Numerical Analysis Pub Date : 2023-12-13 DOI: arxiv-2312.07940

Haiyong Wang, Lun Zhang

引用次数: 0

Computing approximate symmetries of complex networks 计算复杂网络的近似对称性

arXiv - CS - Numerical Analysis Pub Date : 2023-12-13 DOI: arxiv-2312.08042

Anna Pidnebesna, David Hartman, Aneta Pokorná, Matěj Straka, Jaroslav Hlinka

{"title":"Computing approximate symmetries of complex networks","authors":"Anna Pidnebesna, David Hartman, Aneta Pokorná, Matěj Straka, Jaroslav Hlinka","doi":"arxiv-2312.08042","DOIUrl":"https://doi.org/arxiv-2312.08042","url":null,"abstract":"The symmetry of complex networks is a global property that has recently\u0000gained attention since MacArthur et al. 2008 showed that many real-world\u0000networks contain a considerable number of symmetries. These authors work with a\u0000very strict symmetry definition based on the network's automorphism. The\u0000potential problem with this approach is that even a slight change in the\u0000graph's structure can remove or create some symmetry. Recently, Liu 2020\u0000proposed to use an approximate automorphism instead of strict automorphism.\u0000This method can discover symmetries in the network while accepting some minor\u0000imperfections in their structure. The proposed numerical method, however,\u0000exhibits some performance problems and has some limitations while it assumes\u0000the absence of fixed points. In this work, we exploit alternative approaches\u0000recently developed for treating the Graph Matching Problem and propose a\u0000method, which we will refer to as Quadratic Symmetry Approximator (QSA), to\u0000address the aforementioned shortcomings. To test our method, we propose a set\u0000of random graph models suitable for assessing a wide family of approximate\u0000symmetry algorithms. The performance of our method is also demonstrated on\u0000brain networks.","PeriodicalId":501061,"journal":{"name":"arXiv - CS - Numerical Analysis","volume":"31 1","pages":""},"PeriodicalIF":0.0,"publicationDate":"2023-12-13","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"138630314","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}

引用次数: 0

Rectified deep neural networks overcome the curse of dimensionality when approximating solutions of McKean--Vlasov stochastic differential equations 整流深度神经网络在近似麦金--弗拉索夫随机微分方程的解时克服了维度诅咒

arXiv - CS - Numerical Analysis Pub Date : 2023-12-12 DOI: arxiv-2312.07042

Ariel Neufeld, Tuan Anh Nguyen

引用次数: 0

Error Analysis for the Implicit Boundary Integral Method 隐式边界积分法的误差分析

arXiv - CS - Numerical Analysis Pub Date : 2023-12-12 DOI: arxiv-2312.07722

Yimin Zhong, Kui Ren, Olof Runborg, Richard Tsai

引用次数: 0

Discretely Nonlinearly Stable Weight-Adjusted Flux Reconstruction High-Order Method for Compressible Flows on Curvilinear Grids 曲线网格上可压缩流的离散非线性稳定权重调整通量重构高阶方法

arXiv - CS - Numerical Analysis Pub Date : 2023-12-12 DOI: arxiv-2312.07725

Alexander Cicchino, Siva Nadarajah

{"title":"Discretely Nonlinearly Stable Weight-Adjusted Flux Reconstruction High-Order Method for Compressible Flows on Curvilinear Grids","authors":"Alexander Cicchino, Siva Nadarajah","doi":"arxiv-2312.07725","DOIUrl":"https://doi.org/arxiv-2312.07725","url":null,"abstract":"Provable nonlinear stability bounds the discrete approximation and ensures\u0000that the discretization does not diverge. For high-order methods, discrete\u0000nonlinear stability and entropy stability, have been successfully implemented\u0000for discontinuous Galerkin (DG) and residual distribution schemes, where the\u0000stability proofs depend on properties of L2-norms. In this paper, nonlinearly\u0000stable flux reconstruction (NSFR) schemes are developed for three-dimensional\u0000compressible flow in curvilinear coordinates. NSFR is derived by merging the\u0000energy stable FR (ESFR) framework with entropy stable DG schemes. NSFR is\u0000demonstrated to use larger time-steps than DG due to the ESFR correction\u0000functions. NSFR differs from ESFR schemes in the literature since it\u0000incorporates the FR correction functions on the volume terms through the use of\u0000a modified mass matrix. We also prove that discrete kinetic energy stability\u0000cannot be preserved to machine precision for quadrature rules where the surface\u0000quadrature is not a subset of the volume quadrature. This paper also presents\u0000the NSFR modified mass matrix in a weight-adjusted form. This form reduces the\u0000computational cost in curvilinear coordinates through sum-fcatorization and\u0000low-storage techniques. The nonlinear stability properties of the scheme are\u0000verified on a nonsymmetric curvilinear grid for the inviscid Taylor-Green\u0000vortex problem and the correct orders of convergence were obtained for a\u0000manufactured solution. Lastly, we perform a computational cost comparison\u0000between conservative DG, overintegrated DG, and our proposed entropy conserving\u0000NSFR scheme, and find that our proposed entropy conserving NSFR scheme is\u0000computationally competitive with the conservative DG scheme.","PeriodicalId":501061,"journal":{"name":"arXiv - CS - Numerical Analysis","volume":"4 1","pages":""},"PeriodicalIF":0.0,"publicationDate":"2023-12-12","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"138630638","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}

引用次数: 0

Very high order treatment of embedded curved boundaries in compressible flows: ADER discontinuous Galerkin with a space-time Reconstruction for Off-site data 可压缩流中嵌入式曲面边界的极高阶处理：ADER 非连续伽勒金与非现场数据的时空重构

arXiv - CS - Numerical Analysis Pub Date : 2023-12-12 DOI: arxiv-2312.07170

Mirco Ciallella, Stephane Clain, Elena Gaburro, Mario Ricchiuto

{"title":"Very high order treatment of embedded curved boundaries in compressible flows: ADER discontinuous Galerkin with a space-time Reconstruction for Off-site data","authors":"Mirco Ciallella, Stephane Clain, Elena Gaburro, Mario Ricchiuto","doi":"arxiv-2312.07170","DOIUrl":"https://doi.org/arxiv-2312.07170","url":null,"abstract":"In this paper we present a novel approach for the design of high order\u0000general boundary conditions when approximating solutions of the Euler equations\u0000on domains with curved boundaries, using meshes which may not be boundary\u0000conformal. When dealing with curved boundaries and/or unfitted discretizations,\u0000the consistency of boundary conditions is a well-known challenge, especially in\u0000the context of high order schemes. In order to tackle such consistency\u0000problems, the so-called Reconstruction for Off-site Data (ROD) method has been\u0000recently introduced in the finite volume framework: it is based on performing a\u0000boundary polynomial reconstruction that embeds the considered boundary\u0000treatment thanks to the implementation of a constrained minimization problem.\u0000This work is devoted to the development of the ROD approach in the context of\u0000discontinuous finite elements. We use the genuine space-time nature of the\u0000local ADER predictors to reformulate the ROD as a single space-time\u0000reconstruction procedure. This allows us to avoid a new reconstruction (linear\u0000system inversion) at each sub-time node and retrieve a single space-time\u0000polynomial that embeds the considered boundary conditions for the entire\u0000space-time element. Several numerical experiments are presented proving the\u0000consistency of the new approach for all kinds of boundary conditions.\u0000Computations involving the interaction of shocks with embedded curved\u0000boundaries are made possible through an a posteriori limiting technique.","PeriodicalId":501061,"journal":{"name":"arXiv - CS - Numerical Analysis","volume":"86 1","pages":""},"PeriodicalIF":0.0,"publicationDate":"2023-12-12","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"138630206","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}

引用次数: 0

Proving the stability estimates of variational least-squares Kernel-Based methods 证明基于核的变分最小二乘法的稳定性估计值

arXiv - CS - Numerical Analysis Pub Date : 2023-12-12 DOI: arxiv-2312.07080

Meng Chen, Leevan Ling, Dongfang Yun

{"title":"Proving the stability estimates of variational least-squares Kernel-Based methods","authors":"Meng Chen, Leevan Ling, Dongfang Yun","doi":"arxiv-2312.07080","DOIUrl":"https://doi.org/arxiv-2312.07080","url":null,"abstract":"Motivated by the need for the rigorous analysis of the numerical stability of\u0000variational least-squares kernel-based methods for solving second-order\u0000elliptic partial differential equations, we provide previously lacking\u0000stability inequalities. This fills a significant theoretical gap in the\u0000previous work [Comput. Math. Appl. 103 (2021) 1-11], which provided error\u0000estimates based on a conjecture on the stability. With the stability estimate\u0000now rigorously proven, we complete the theoretical foundations and compare the\u0000convergence behavior to the proven rates. Furthermore, we establish another\u0000stability inequality involving weighted-discrete norms, and provide a\u0000theoretical proof demonstrating that the exact quadrature weights are not\u0000necessary for the weighted least-squares kernel-based collocation method to\u0000converge. Our novel theoretical insights are validated by numerical examples,\u0000which showcase the relative efficiency and accuracy of these methods on data\u0000sets with large mesh ratios. The results confirm our theoretical predictions\u0000regarding the performance of variational least-squares kernel-based method,\u0000least-squares kernel-based collocation method, and our new weighted\u0000least-squares kernel-based collocation method. Most importantly, our results\u0000demonstrate that all methods converge at the same rate, validating the\u0000convergence theory of weighted least-squares in our proven theories.","PeriodicalId":501061,"journal":{"name":"arXiv - CS - Numerical Analysis","volume":"169 1","pages":""},"PeriodicalIF":0.0,"publicationDate":"2023-12-12","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"138630149","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}

引用次数: 0

Rational Approximations for Oscillatory Two-Parameter Mittag-Leffler Function 振荡双参数 Mittag-Leffler 函数的有理近似值

arXiv - CS - Numerical Analysis Pub Date : 2023-12-12 DOI: arxiv-2312.07444

Aljowhara H. Honain, Khaled M. Furati, Ibrahim O. Sarumi, Abdul Q. M. Khaliq

{"title":"Rational Approximations for Oscillatory Two-Parameter Mittag-Leffler Function","authors":"Aljowhara H. Honain, Khaled M. Furati, Ibrahim O. Sarumi, Abdul Q. M. Khaliq","doi":"arxiv-2312.07444","DOIUrl":"https://doi.org/arxiv-2312.07444","url":null,"abstract":"The two-parameter Mittag-Leffler function $E_{alpha, beta}$ is of\u0000fundamental importance in fractional calculus. It appears frequently in the\u0000solutions of fractional differential and integral equations. Nonetheless, this\u0000vital function is often expensive to compute. Several attempts have been made\u0000to construct cost-effective and accurate approximations. These attempts focus\u0000mainly on the completely monotone Mittag-Leffler functions. However, when\u0000$alpha > 1$ the monotonicity property is largely lost and as such roots and\u0000oscillations are exhibited. Consequently, existing approximants constructed\u0000mainly for $alpha in (0,1)$ often fail to capture this oscillatory behavior.\u0000In this paper, we construct computationally efficient and accurate rational\u0000approximants for $E_{alpha, beta}(-t)$, $t ge 0$, with $alpha in (1,2)$.\u0000This construction is fundamentally based on the decomposition of Mittag-Leffler\u0000function with real roots into one without and a polynomial. Following which new\u0000approximants are constructed by combining the global Pad'e approximation with\u0000a polynomial of appropriate degree. The rational approximants are extended to\u0000approximation of matrix Mittag-Leffler and different approaches to achieve\u0000efficient implementation for matrix arguments are discussed. Numerical\u0000experiments are provided to illustrate the significant accuracy improvement\u0000achieved by the proposed approximants.","PeriodicalId":501061,"journal":{"name":"arXiv - CS - Numerical Analysis","volume":"7 1","pages":""},"PeriodicalIF":0.0,"publicationDate":"2023-12-12","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"138629921","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}

引用次数: 0

Splitting ADI scheme for fractional Laplacian wave equations 分数拉普拉斯波方程的 ADI 方案分裂

arXiv - CS - Numerical Analysis Pub Date : 2023-12-11 DOI: arxiv-2312.06206

Tao Sun, Hai-Wei Sun

引用次数: 0