Numerical Algorithms最新文献_第9页

On certain matrix algebras related to quasi-Toeplitz matrices 关于与准托普利兹矩阵有关的某些矩阵代数

IF 2.1 3区数学

Numerical Algorithms Pub Date : 2024-06-13 DOI: 10.1007/s11075-024-01855-3

Dario A. Bini, Beatrice Meini

{"title":"On certain matrix algebras related to quasi-Toeplitz matrices","authors":"Dario A. Bini, Beatrice Meini","doi":"10.1007/s11075-024-01855-3","DOIUrl":"https://doi.org/10.1007/s11075-024-01855-3","url":null,"abstract":"Let (A_alpha ) be the semi-infinite tridiagonal matrix having subdiagonal and superdiagonal unit entries, ((A_alpha )_{11}=alpha ), where (alpha in mathbb C), and zero elsewhere. A basis ({P_0,P_1,P_2,ldots }) of the linear space (mathcal {P}_alpha ) spanned by the powers of (A_alpha ) is determined, where (P_0=I), (P_n=T_n+H_n), (T_n) is the symmetric Toeplitz matrix having ones in the nth super- and sub-diagonal, zeros elsewhere, and (H_n) is the Hankel matrix with first row ([theta alpha ^{n-2}, theta alpha ^{n-3}, ldots , theta , alpha , 0, ldots ]), where (theta =alpha ^2-1). The set (mathcal {P}_alpha ) is an algebra, and for (alpha in {-1,0,1}), (H_n) has only one nonzero anti-diagonal. This fact is exploited to provide a better representation of symmetric quasi-Toeplitz matrices (mathcal{Q}mathcal{T}_S), where, instead of representing a generic matrix (Ain mathcal{Q}mathcal{T}_S) as (A=T+K), where T is Toeplitz and K is compact, it is represented as (A=P+H), where (Pin mathcal {P}_alpha ) and H is compact. It is shown experimentally that the matrix arithmetic obtained this way is much more effective than that implemented in the toolbox CQT-Toolbox of Numer. Algo. 81(2):741–769, 2019.","PeriodicalId":54709,"journal":{"name":"Numerical Algorithms","volume":"32 1","pages":""},"PeriodicalIF":2.1,"publicationDate":"2024-06-13","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"141514531","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 solutions of the EW and MEW equations using a fourth-order improvised B-spline collocation method 使用四阶简易 B-样条配位法数值求解 EW 和 MEW 方程

IF 2.1 3区数学

Numerical Algorithms Pub Date : 2024-06-05 DOI: 10.1007/s11075-024-01853-5

Guangyu Fan, Beibei Wu

{"title":"Numerical solutions of the EW and MEW equations using a fourth-order improvised B-spline collocation method","authors":"Guangyu Fan, Beibei Wu","doi":"10.1007/s11075-024-01853-5","DOIUrl":"https://doi.org/10.1007/s11075-024-01853-5","url":null,"abstract":"A fourth-order improvised cubic B-spline collocation method (ICSCM) is proposed to numerically solve the equal width (EW) equation and the modified equal width (MEW) equation. The discretization of the spatial domain is done using the ICSCM and the Crank-Nicolson scheme is used for the discretization of the temporal domain. The nonlinear terms are processed using quasi-linearization techniques and the stability analysis of this method is performed using Fourier series analysis. The validity and accuracy of this method are verified through several numerical experiments using a single solitary wave, two solitary waves, Maxwellian initial condition, and an undular bore. Since there is an exact solution for the single wave, the error norms (varvec{L_2}) and (varvec{L_{infty }}) are first calculated and compared with some previous studies published in journal articles. In addition, the three conserved quantities (varvec{Q}), (varvec{M}), and (varvec{E}) of the problems raised during the simulation are also calculated and recorded in the table. Lastly, the comparisons of these error norms and conserved quantities show that the numerical results obtained with the proposed method are more accurate and agree well with the values of the conserved quantities obtained in some literatures using the same parameters. The main advantage of ICSCM is its ability to effectively capture solitary wave propagation and describe solitary wave collisions. It can perform solution calculations at any point in the domain, easily use larger time steps to calculate solutions at higher time levels, and produce more accurate calculation results.","PeriodicalId":54709,"journal":{"name":"Numerical Algorithms","volume":"41 1","pages":""},"PeriodicalIF":2.1,"publicationDate":"2024-06-05","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"141252794","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

Modified projection method and strong convergence theorem for solving variational inequality problems with non-Lipschitz operators 解决非 Lipschitz 算子的变分不等式问题的修正投影法和强收敛定理

IF 2.1 3区数学

Numerical Algorithms Pub Date : 2024-06-01 DOI: 10.1007/s11075-024-01851-7

Zhongbing Xie, Huanqin Wu, Liya Liu

引用次数: 0

ANODE 2023 In honour of John Butcher’s 90th birthday ANODE 2023 纪念约翰-布彻 90 岁生日

IF 2.1 3区数学

Numerical Algorithms Pub Date : 2024-05-31 DOI: 10.1007/s11075-024-01849-1

Kevin Burrage, Zdzisław Jackiewicz, Bernd Krauskopf, Yuto Miyatake, Helmut Podhaisky, Mayya Tokman

引用次数: 0

C-FISTA type projection algorithm for quasi-variational inequalities 准变不等式的 C-FISTA 型投影算法

IF 2.1 3区数学

Numerical Algorithms Pub Date : 2024-05-30 DOI: 10.1007/s11075-024-01852-6

Yonghong Yao, Lateef O. Jolaoso, Yekini Shehu

引用次数: 0

Two novel numerical methods for gradient flows: generalizations of the Invariant Energy Quadratization method 梯度流的两种新型数值方法：不变能量四分法的一般化

IF 2.1 3区数学

Numerical Algorithms Pub Date : 2024-05-30 DOI: 10.1007/s11075-024-01847-3

Yukun Yue

引用次数: 0

Operator-splitting finite element method for solving the radiative transfer equation 用于求解辐射传递方程的算子分裂有限元法

IF 2.1 3区数学

Numerical Algorithms Pub Date : 2024-05-29 DOI: 10.1007/s11075-024-01850-8

Sashikumaar Ganesan, Maneesh Kumar Singh

引用次数: 0

Boundary reconstruction in two-dimensional steady-state anisotropic heat conduction 二维稳态各向异性热传导中的边界重构

IF 2.1 3区数学

Numerical Algorithms Pub Date : 2024-05-29 DOI: 10.1007/s11075-024-01831-x

Liviu Marin, Andrei Tiberiu Pantea

{"title":"Boundary reconstruction in two-dimensional steady-state anisotropic heat conduction","authors":"Liviu Marin, Andrei Tiberiu Pantea","doi":"10.1007/s11075-024-01831-x","DOIUrl":"https://doi.org/10.1007/s11075-024-01831-x","url":null,"abstract":"We study the reconstruction of an unknown/inaccessible smooth inner boundary from the knowledge of the Dirichlet condition (temperature) on the entire boundary of a doubly connected domain occupied by a two-dimensional homogeneous anisotropic solid and an additional Neumann condition (normal heat flux) on the known, accessible, and smooth outer boundary in the framework of steady-state heat conduction with heat sources. This inverse geometric problem is approached through an operator that maps an admissible inner boundary belonging to the space of (2pi -)periodic and twice continuously differentiable functions into the Neumann data on the outer boundary which is assumed to be continuous. We prove that this operator is differentiable, and hence, a gradient-based method that employs the anisotropic single layer representation of the solution to an appropriate Dirichlet problem for the two-dimensional anisotropic heat conduction is developed for approximating the unknown inner boundary. Numerical results are presented for both exact and perturbed Neumann data on the outer boundary and show the convergence, stability, and robustness of the proposed method.","PeriodicalId":54709,"journal":{"name":"Numerical Algorithms","volume":"44 1","pages":""},"PeriodicalIF":2.1,"publicationDate":"2024-05-29","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"141168715","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

Delay-dependent stability of a class of Runge-Kutta methods for neutral differential equations 一类中性微分方程 Runge-Kutta 方法的延迟稳定性

IF 2.1 3区数学

Numerical Algorithms Pub Date : 2024-05-18 DOI: 10.1007/s11075-024-01846-4

Zheng Wang, Yuhao Cong

引用次数: 0

Quantile-based random sparse Kaczmarz for corrupted and noisy linear systems 基于量子的随机稀疏 Kaczmarz，适用于损坏和噪声线性系统

IF 2.1 3区数学

Numerical Algorithms Pub Date : 2024-05-13 DOI: 10.1007/s11075-024-01844-6

Lu Zhang, Hongxia Wang, Hui Zhang

引用次数: 0