Numerical Algorithms最新文献_第9页

General double-relaxation two-sweep modulus-based matrix splitting iteration methods for horizontal linear complementarity problem 针对水平线性互补问题的基于模数的通用双松弛两扫矩阵分割迭代法

IF 2.1 3区数学

Numerical Algorithms Pub Date : 2024-06-25 DOI: 10.1007/s11075-024-01860-6

Dan Wang, Jicheng Li

引用次数: 0

Spectral characterizations and integer powers of tridiagonal 2-Toeplitz matrices 三对角 2-Toeplitz 矩阵的谱特征和整数幂

IF 2.1 3区数学

Numerical Algorithms Pub Date : 2024-06-22 DOI: 10.1007/s11075-024-01863-3

Maryam Shams Solary, Stefano Serra-Capizzano

引用次数: 0

Convergence analysis of Picard–SP iteration process for generalized $$alpha $$ –nonexpansive mappings 广义$$alpha$$无穷映射的Picard-SP迭代过程收敛性分析

IF 2.1 3区数学

Numerical Algorithms Pub Date : 2024-06-18 DOI: 10.1007/s11075-024-01859-z

Bashir Nawaz, Kifayat Ullah, Krzysztof Gdawiec

引用次数: 0

$$L^2$$ norm convergence of IMEX BDF2 scheme with variable-step for the incompressible Navier-Stokes equations 不可压缩纳维-斯托克斯方程的变步长 IMEX BDF2 方案的 $L^2$$ 规范收敛性

IF 2.1 3区数学

Numerical Algorithms Pub Date : 2024-06-17 DOI: 10.1007/s11075-024-01858-0

Bingquan Ji, Xuan Zhao

{"title":"$$L^2$$ norm convergence of IMEX BDF2 scheme with variable-step for the incompressible Navier-Stokes equations","authors":"Bingquan Ji, Xuan Zhao","doi":"10.1007/s11075-024-01858-0","DOIUrl":"https://doi.org/10.1007/s11075-024-01858-0","url":null,"abstract":"We present an (L^2) norm convergence of the implicit-explicit BDF2 scheme with variable-step for the unsteady incompressible Navier-Stokes equations with an inf-sup stable FEM for the space discretization. Under a weak step-ratio constraint (0<r_k:=tau _k/tau _{k-1}<4.864), our error estimate is mesh-robust in the sense that it completely removes the possibly unbounded quantities, such as (Gamma _N=sum _{k=1}^{N-2}max {0,r_{k}-r_{k+2}}) and (Lambda _N=sum _{k=1}^{N-1}(|r_{k}-1|+|r_{k+1}-1|)) included in previous studies. In this analysis, we integrate our recent theoretical framework that employs discrete orthogonal convolution (DOC) kernels with an auxiliary Stokes problem to split the convergence analysis into two distinct parts. In the first part, we address intricate consistency error estimates for the velocity, pressure and nonlinear convection term. The resulting estimates allow us to utilize the conventional methodologies within the DOC framework to preserve spatial accuracy. In the second part, through the use of the DOC technique, we prove that the proposed variable-step BDF2 scheme is of second-order accuracy in time with respect to the (L^2) norm. Extensive numerical simulations coupled with an adaptive time-stepping algorithm are performed to show the accuracy and efficiency of the proposed variable-step method for the incompressible flows.","PeriodicalId":54709,"journal":{"name":"Numerical Algorithms","volume":null,"pages":null},"PeriodicalIF":2.1,"publicationDate":"2024-06-17","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"141514530","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

Solving a system of complex matrix equations using a gradient-based method and its application in image restoration 使用基于梯度的方法求解复杂矩阵方程组及其在图像复原中的应用

IF 2.1 3区数学

Numerical Algorithms Pub Date : 2024-06-15 DOI: 10.1007/s11075-024-01856-2

Akbar Shirilord, Mehdi Dehghan

引用次数: 0

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":null,"pages":null},"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

Two-level methods for solving higher order finite element discretizations of nonsymmetric and indefinite elliptic problem 解决非对称和不定椭圆问题高阶有限元离散化的两级方法

IF 2.1 3区数学

Numerical Algorithms Pub Date : 2024-06-08 DOI: 10.1007/s11075-024-01857-1

Liuqiang Zhong, Huilan Li, Ming Tang

引用次数: 0

On solving 2D weakly singular Volterra integral equations of the second kind 关于求解二维弱奇异 Volterra 第二类积分方程

IF 2.1 3区数学

Numerical Algorithms Pub Date : 2024-06-07 DOI: 10.1007/s11075-024-01854-4

Y. Chakir, H. Safouhi

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":null,"pages":null},"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