Numerical Linear Algebra with Applications最新文献_第5页

Numerical methods for rectangular multiparameter eigenvalue problems, with applications to finding optimal ARMA and LTI models 矩形多参数特征值问题的数值方法，并应用于寻找最优ARMA和LTI模型

3区数学

Numerical Linear Algebra with Applications Pub Date : 2023-11-09 DOI: 10.1002/nla.2540

Michiel E. Hochstenbach, Tomaž Košir, Bor Plestenjak

{"title":"Numerical methods for rectangular multiparameter eigenvalue problems, with applications to finding optimal ARMA and LTI models","authors":"Michiel E. Hochstenbach, Tomaž Košir, Bor Plestenjak","doi":"10.1002/nla.2540","DOIUrl":"https://doi.org/10.1002/nla.2540","url":null,"abstract":"Abstract Standard multiparameter eigenvalue problems (MEPs) are systems of linear ‐parameter square matrix pencils. Recently, a new form of multiparameter eigenvalue problems has emerged: a rectangular MEP (RMEP) with only one multivariate rectangular matrix pencil, where we are looking for combinations of the parameters for which the rank of the pencil is not full. Applications include finding the optimal least squares autoregressive moving average (ARMA) model and the optimal least squares realization of autonomous linear time‐invariant (LTI) dynamical system. For linear and polynomial RMEPs, we give the number of solutions and show how these problems can be solved numerically by a transformation into a standard MEP. For the transformation we provide new linearizations for quadratic multivariate matrix polynomials with a specific structure of monomials and consider mixed systems of rectangular and square multivariate matrix polynomials. This numerical approach seems computationally considerably more attractive than the block Macaulay method, the only other currently available numerical method for polynomial RMEPs.","PeriodicalId":49731,"journal":{"name":"Numerical Linear Algebra with Applications","volume":null,"pages":null},"PeriodicalIF":0.0,"publicationDate":"2023-11-09","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"135242136","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

Bringing physics into the coarse‐grid selection: Approximate diffusion distance/effective resistance measures for network analysis and algebraic multigrid for graph Laplacians and systems of elliptic partial differential equations 将物理学引入粗网格选择:网络分析的近似扩散距离/有效阻力措施以及图拉普拉斯算子和椭圆偏微分方程系统的代数多重网格

3区数学

Numerical Linear Algebra with Applications Pub Date : 2023-11-02 DOI: 10.1002/nla.2539

Barry Lee

{"title":"Bringing physics into the coarse‐grid selection: Approximate diffusion distance/effective resistance measures for network analysis and algebraic multigrid for graph Laplacians and systems of elliptic partial differential equations","authors":"Barry Lee","doi":"10.1002/nla.2539","DOIUrl":"https://doi.org/10.1002/nla.2539","url":null,"abstract":"Abstract In a recent paper, the author examined a correlation affinity measure for selecting the coarse degrees of freedom (CDOFs) or coarse nodes (C nodes) in systems of elliptic partial differential equations (PDEs). This measure was applied to a set of relaxed vectors, which exposed the near‐nullspace components of the PDE operator. Selecting the CDOFs using this affinity measure and constructing the interpolation operators using a least‐squares procedure, an algebraic multigrid (AMG) method was developed. However, there are several noted issues with this AMG solver. First, to capture strong anisotropies, a large number of test vectors may be needed; and second, the solver's performance can be sensitive to the initial set of random test vectors. Both issues reflect the sensitive statistical nature of the measure. In this article, we derive several other statistical measures that ameliorate these issues and lead to better AMG performance. These measures are related to a Markov process, which the PDE itself may model. Specifically, the measures are based on the diffusion distance/effective resistance for such process, and hence, these measures incorporate physics into the CDOF selection. Moreover, because the diffusion distance/effective resistance can be used to analyze graph networks, these measures also provide a very economical scheme for analyzing large‐scale networks. In this article, the derivations of these measures are given, and numerical experiments for analyzing networks and for AMG performance on weighted‐graph Laplacians and systems of elliptic boundary‐value problems are presented.","PeriodicalId":49731,"journal":{"name":"Numerical Linear Algebra with Applications","volume":null,"pages":null},"PeriodicalIF":0.0,"publicationDate":"2023-11-02","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"135974107","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

Shifted LOPBiCG: A locally orthogonal product‐type method for solving nonsymmetric shifted linear systems based on Bi‐CGSTAB 移位LOPBiCG:基于Bi‐CGSTAB的求解非对称移位线性系统的局部正交积型方法

3区数学

Numerical Linear Algebra with Applications Pub Date : 2023-10-30 DOI: 10.1002/nla.2538

Ren‐Jie Zhao, Tomohiro Sogabe, Tomoya Kemmochi, Shao‐Liang Zhang

引用次数: 0

Algebra preconditionings for 2D Riesz distributed‐order space‐fractional diffusion equations on convex domains 凸域上二维Riesz分布阶空间分数扩散方程的代数前提

3区数学

Numerical Linear Algebra with Applications Pub Date : 2023-10-23 DOI: 10.1002/nla.2536

Mariarosa Mazza, Stefano Serra‐Capizzano, Rosita Luisa Sormani

{"title":"Algebra preconditionings for 2D Riesz distributed‐order space‐fractional diffusion equations on convex domains","authors":"Mariarosa Mazza, Stefano Serra‐Capizzano, Rosita Luisa Sormani","doi":"10.1002/nla.2536","DOIUrl":"https://doi.org/10.1002/nla.2536","url":null,"abstract":"Abstract When dealing with the discretization of differential equations on non‐rectangular domains, a careful treatment of the boundary is mandatory and may result in implementation difficulties and in coefficient matrices without a prescribed structure. Here we examine the numerical solution of a two‐dimensional constant coefficient distributed‐order space‐fractional diffusion equation with a nonlinear term on a convex domain. To avoid the aforementioned inconvenience, we resort to the volume‐penalization method, which consists of embedding the domain into a rectangle and in adding a reaction penalization term to the original equation that dominates in the region outside the original domain and annihilates the solution correspondingly. Thanks to the volume‐penalization, methods designed for problems in rectangular domains are available for those in convex domains and by applying an implicit finite difference scheme we obtain coefficient matrices with a 2‐level Toeplitz structure plus a diagonal matrix which arises from the penalty term. As a consequence of the latter, we can describe the asymptotic eigenvalue distribution as the matrix size diverges as well as estimate the intrinsic asymptotic ill‐conditioning of the involved matrices. On these bases, we discuss the performances of the conjugate gradient with circulant and ‐preconditioners and of the generalized minimal residual with split circulant and ‐preconditioners and conduct related numerical experiments.","PeriodicalId":49731,"journal":{"name":"Numerical Linear Algebra with Applications","volume":null,"pages":null},"PeriodicalIF":0.0,"publicationDate":"2023-10-23","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"135405491","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

Quasi‐Newton variable preconditioning for nonlinear elasticity systems in 3D 三维非线性弹性系统的准牛顿变量预处理

3区数学

Numerical Linear Algebra with Applications Pub Date : 2023-10-23 DOI: 10.1002/nla.2537

J. Karátson, S. Sysala, M. Béreš

引用次数: 0

A tensor bidiagonalization method for higher‐order singular value decomposition with applications 高阶奇异值分解的张量双对角化方法及其应用

3区数学

Numerical Linear Algebra with Applications Pub Date : 2023-10-01 DOI: 10.1002/nla.2530

A. El Hachimi, K. Jbilou, A. Ratnani, L. Reichel

引用次数: 0

A conforming auxiliary space preconditioner for the mass conserving stress-yielding method. 质量守恒应力屈服法的协调辅助空间预处理器

IF 1.8 3区数学

Numerical Linear Algebra with Applications Pub Date : 2023-10-01 Epub Date: 2023-05-07 DOI: 10.1002/nla.2503

Lukas Kogler, Philip L Lederer, Joachim Schöberl

引用次数: 0

Computing the completely positive factorization via alternating minimization 通过交替最小化计算完全正分解

3区数学

Numerical Linear Algebra with Applications Pub Date : 2023-09-28 DOI: 10.1002/nla.2535

R. Behling, H. Lara, H. Oviedo

引用次数: 0

Conditioning of hybrid variational data assimilation 混合变分数据同化的条件作用

3区数学

Numerical Linear Algebra with Applications Pub Date : 2023-09-26 DOI: 10.1002/nla.2534

Shaerdan Shataer, Amos S. Lawless, Nancy K. Nichols

{"title":"Conditioning of hybrid variational data assimilation","authors":"Shaerdan Shataer, Amos S. Lawless, Nancy K. Nichols","doi":"10.1002/nla.2534","DOIUrl":"https://doi.org/10.1002/nla.2534","url":null,"abstract":"Abstract In variational assimilation, the most probable state of a dynamical system under Gaussian assumptions for the prior and likelihood can be found by solving a least‐squares minimization problem. In recent years, we have seen the popularity of hybrid variational data assimilation methods for Numerical Weather Prediction. In these methods, the prior error covariance matrix is a weighted sum of a climatological part and a flow‐dependent ensemble part, the latter being rank deficient. The nonlinear least squares problem of variational data assimilation is solved using iterative numerical methods, and the condition number of the Hessian is a good proxy for the convergence behavior of such methods. In this article, we study the conditioning of the least squares problem in a hybrid four‐dimensional variational data assimilation (Hybrid 4D‐Var) scheme by establishing bounds on the condition number of the Hessian. In particular, we consider the effect of the ensemble component of the prior covariance on the conditioning of the system. Numerical experiments show that the bounds obtained can be useful in predicting the behavior of the true condition number and the convergence speed of an iterative algorithm","PeriodicalId":49731,"journal":{"name":"Numerical Linear Algebra with Applications","volume":null,"pages":null},"PeriodicalIF":0.0,"publicationDate":"2023-09-26","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"134958103","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

A family of inertial‐based derivative‐free projection methods with a correction step for constrained nonlinear equations and their applications 一类基于惯性的无导数投影法及其应用

3区数学

Numerical Linear Algebra with Applications Pub Date : 2023-09-22 DOI: 10.1002/nla.2533

Pengjie Liu, Hu Shao, Zihang Yuan, Jianhao Zhou

{"title":"A family of inertial‐based derivative‐free projection methods with a correction step for constrained nonlinear equations and their applications","authors":"Pengjie Liu, Hu Shao, Zihang Yuan, Jianhao Zhou","doi":"10.1002/nla.2533","DOIUrl":"https://doi.org/10.1002/nla.2533","url":null,"abstract":"Abstract Numerous attempts have been made to develop efficient methods for solving the system of constrained nonlinear equations due to its widespread use in diverse engineering applications. In this article, we present a family of inertial‐based derivative‐free projection methods with a correction step for solving such system, in which the selection of the derivative‐free search direction is flexible. This family does not require the computation of corresponding Jacobian matrix or approximate matrix at every iteration and possess the following theoretical properties: (i) the inertial‐based corrected direction framework always automatically satisfies the sufficient descent and trust region properties without specific search directions, and is independent of any line search; (ii) the global convergence of the proposed family is proven under a weaker monotonicity condition on the mapping , without the typical monotonicity or pseudo‐monotonicity assumption; (iii) the results about convergence rate of the proposed family are established under slightly stronger assumptions. Furthermore, we propose two effective inertial‐based derivative‐free projection methods, each embedding a specific search direction into the proposed family. We present preliminary numerical experiments on certain test problems to demonstrate the effectiveness and superiority of the proposed methods in comparison with existing ones. Additionally, we utilize these methods for solving sparse signal restorations and image restorations in compressive sensing applications.","PeriodicalId":49731,"journal":{"name":"Numerical Linear Algebra with Applications","volume":null,"pages":null},"PeriodicalIF":0.0,"publicationDate":"2023-09-22","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"136060602","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