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Inertial randomized Kaczmarz algorithms for solving coherent linear systems 求解相干线性系统的惯性随机卡兹马兹算法
IF 2.1 3区 数学
Numerical Algorithms Pub Date : 2024-07-05 DOI: 10.1007/s11075-024-01872-2
Songnian He, Ziting Wang, Qiao-Li Dong
{"title":"Inertial randomized Kaczmarz algorithms for solving coherent linear systems","authors":"Songnian He, Ziting Wang, Qiao-Li Dong","doi":"10.1007/s11075-024-01872-2","DOIUrl":"https://doi.org/10.1007/s11075-024-01872-2","url":null,"abstract":"<p>In this paper, by regarding the two-subspace Kaczmarz method as an alternated inertial randomized Kaczmarz algorithm we present a better convergence rate estimate under a mild condition. Furthermore, we accelerate the alternated inertial randomized Kaczmarz algorithm and introduce a multi-step inertial randomized Kaczmarz algorithm which is proved to have a faster convergence rate. Numerical experiments support the theory results and illustrate that the multi-inertial randomized Kaczmarz algorithm significantly outperform the two-subspace Kaczmarz method in solving coherent linear systems.</p>","PeriodicalId":54709,"journal":{"name":"Numerical Algorithms","volume":null,"pages":null},"PeriodicalIF":2.1,"publicationDate":"2024-07-05","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"141550524","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
Caputo fractional derivative of $$alpha $$ -fractal spline 分形样条曲线的卡普托分数导数
IF 2.1 3区 数学
Numerical Algorithms Pub Date : 2024-07-05 DOI: 10.1007/s11075-024-01875-z
T. M. C. Priyanka, A. Gowrisankar, M. Guru Prem Prasad, Yongshun Liang, Jinde Cao
{"title":"Caputo fractional derivative of $$alpha $$ -fractal spline","authors":"T. M. C. Priyanka, A. Gowrisankar, M. Guru Prem Prasad, Yongshun Liang, Jinde Cao","doi":"10.1007/s11075-024-01875-z","DOIUrl":"https://doi.org/10.1007/s11075-024-01875-z","url":null,"abstract":"<p>The Caputo fractional derivative of a real continuous function <i>g</i> distinguishes from the other fractional derivative methods with the demand for the existence of its first order derivative <span>(g')</span>. This attribute leads to the investigation of Caputo fractional derivative of <span>(alpha )</span>-fractal splines rather than just a continuous non-differentiable <span>(alpha )</span>-fractal function. A bounded linear operator corresponding to the Caputo fractional derivative of fractal version is reported. In addition, a new family of fractal perturbations is proposed in association with the fractional derivative. Thereafter, a numerical approach is used to determine the exact Caputo fractional derivative of fractal functions in terms of Legendre polynomials.</p>","PeriodicalId":54709,"journal":{"name":"Numerical Algorithms","volume":null,"pages":null},"PeriodicalIF":2.1,"publicationDate":"2024-07-05","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"141550523","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
On the convergence of Galerkin methods for auto-convolution Volterra integro-differential equations 论自动卷积 Volterra 积分微分方程 Galerkin 方法的收敛性
IF 2.1 3区 数学
Numerical Algorithms Pub Date : 2024-07-04 DOI: 10.1007/s11075-024-01874-0
Yuping Li, Hui Liang, Huifang Yuan
{"title":"On the convergence of Galerkin methods for auto-convolution Volterra integro-differential equations","authors":"Yuping Li, Hui Liang, Huifang Yuan","doi":"10.1007/s11075-024-01874-0","DOIUrl":"https://doi.org/10.1007/s11075-024-01874-0","url":null,"abstract":"<p>The Galerkin method is proposed for initial value problem of auto-convolution Volterra integro-differential equation (AVIDE). The solvability of the Galerkin method is discussed, and the uniform boundedness of the numerical solution is provided by defining a discrete weighted exponential norm. In particular, it is proved that the quadrature Galerkin method obtained from the Galerkin method by approximating the inner products by suitable numerical quadrature formulas, is equivalent to the continuous piecewise polynomial collocation method. For the Galerkin approximated solution in continuous piecewise polynomial space of degree <span>(varvec{m})</span>, at first, the <span>(varvec{m})</span> global convergence order is obtained. By defining a projection operator, the convergence is improved, and the optimal <span>(varvec{m+1})</span> global convergence order is gained, as well as <span>(varvec{2m})</span> local convergence order at mesh points. Furthermore, all the above analysis for uniform mesh can be extended to typical quasi-uniform meshes. Some numerical experiments are given to illustrate the theoretical results.</p>","PeriodicalId":54709,"journal":{"name":"Numerical Algorithms","volume":null,"pages":null},"PeriodicalIF":2.1,"publicationDate":"2024-07-04","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"141550525","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 new splitting mixed finite element analysis of the viscoelastic wave equation 粘弹性波方程的新型分裂混合有限元分析
IF 2.1 3区 数学
Numerical Algorithms Pub Date : 2024-07-04 DOI: 10.1007/s11075-024-01876-y
Jiansong Zhang, Liping Gao, Yuanshuo Kong, Mei Wang, Guanqi Yang
{"title":"A new splitting mixed finite element analysis of the viscoelastic wave equation","authors":"Jiansong Zhang, Liping Gao, Yuanshuo Kong, Mei Wang, Guanqi Yang","doi":"10.1007/s11075-024-01876-y","DOIUrl":"https://doi.org/10.1007/s11075-024-01876-y","url":null,"abstract":"<p>This paper aims to propose a new splitting mixed finite element method (MFE) for solving viscoelastic wave equations and give convergence analysis. First, by introducing two new variables <span>(q=u_t)</span> and <span>(varvec{sigma }=A(x)nabla u+B(x)nabla u_t)</span>, a new system of first-order differential-integral equations is derived from the original second-order viscoelastic wave equation. Then, the semi-discrete and fully-discrete splitting MFE schemes are proposed by using the MFE spaces and the second-order time discetization. By the two schemes the approximate solutions for the unknowns <i>u</i>, <span>(u_t)</span> and <span>(sigma )</span> are obtained simultaneously. It is proved that the semi-discrete and fully-discrete schemes have the optimal error estimates in <span>(L^2)</span>-norm. Meanwhile, it is proved that the fully-discrete SMFE scheme based on the Raviart-Thomas mixed finite element spaces and the uniform rectangular mesh partitions is super convergent. Finally, numerical experiments to compute the <span>(L^2)</span> errors for approximating <i>u</i>, <i>q</i> and <span>(varvec{sigma })</span> and their convergence rates are presented, and the theoretical analysis on error estimates and convergence is then confirmed.</p>","PeriodicalId":54709,"journal":{"name":"Numerical Algorithms","volume":null,"pages":null},"PeriodicalIF":2.1,"publicationDate":"2024-07-04","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"141550526","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
On zero behavior of higher-order Sobolev-type discrete $$q-$$ Hermite I orthogonal polynomials 论高阶索波列夫型离散 $$q-$$ 赫米特 I 正交多项式的零点行为
IF 2.1 3区 数学
Numerical Algorithms Pub Date : 2024-07-02 DOI: 10.1007/s11075-024-01868-y
Edmundo J. Huertas, Alberto Lastra, Anier Soria-Lorente, Víctor Soto-Larrosa
{"title":"On zero behavior of higher-order Sobolev-type discrete $$q-$$ Hermite I orthogonal polynomials","authors":"Edmundo J. Huertas, Alberto Lastra, Anier Soria-Lorente, Víctor Soto-Larrosa","doi":"10.1007/s11075-024-01868-y","DOIUrl":"https://doi.org/10.1007/s11075-024-01868-y","url":null,"abstract":"<p>In this work, we investigate the sequence of monic <i>q</i>-Hermite I-Sobolev type orthogonal polynomials of higher-order, denoted by <span>({mathbb {H}_{n}(x;q)}_{nge 0})</span>, which are orthogonal with respect to the following non-standard inner product involving <i>q</i>-differences: </p><span>$$begin{aligned} langle p,qrangle _{lambda }=int _{-1}^{1}fleft( xright) gleft( xright) (qx,-qx;q)_{infty }d_{q}(x)+lambda ,(mathscr {D}_{q}^{j}f)(alpha )(mathscr {D}_{q}^{j}g)(alpha ), end{aligned}$$</span><p>where <span>(lambda )</span> belongs to the set of positive real numbers, <span>(mathscr {D}_{q}^{j})</span> denotes the <i>j</i>-th <i>q</i> -discrete analogue of the derivative operator, <span>(q^jalpha in mathbb {R}backslash (-1,1))</span>, and <span>((qx,-qx;q)_{infty }d_{q}(x))</span> denotes the orthogonality weight with its points of increase in a geometric progression. Connection formulas between these polynomials and standard <i>q</i>-Hermite I polynomials are deduced. The basic hypergeometric representation of <span>(mathbb {H}_{n}(x;q))</span> is obtained. Moreover, for certain real values of <span>(alpha )</span> satisfying the condition <span>(q^jalpha in mathbb {R}backslash (-1,1))</span>, we present results concerning the location of the zeros of <span>(mathbb {H}_{n}(x;q))</span> and perform a comprehensive analysis of their asymptotic behavior as the parameter <span>(lambda )</span> tends to infinity.</p>","PeriodicalId":54709,"journal":{"name":"Numerical Algorithms","volume":null,"pages":null},"PeriodicalIF":2.1,"publicationDate":"2024-07-02","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"141514528","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
Efficient iterative procedures for approximating fixed points of contractive-type mappings with applications 近似收缩型映射定点的高效迭代程序及其应用
IF 2.1 3区 数学
Numerical Algorithms Pub Date : 2024-07-01 DOI: 10.1007/s11075-024-01869-x
Puneet Sharma, Higinio Ramos, Vinay Kanwar, Ramandeep Behl, Mithil Rajput
{"title":"Efficient iterative procedures for approximating fixed points of contractive-type mappings with applications","authors":"Puneet Sharma, Higinio Ramos, Vinay Kanwar, Ramandeep Behl, Mithil Rajput","doi":"10.1007/s11075-024-01869-x","DOIUrl":"https://doi.org/10.1007/s11075-024-01869-x","url":null,"abstract":"<p>This paper introduces and analyzes some new highly efficient iterative procedures for approximating fixed points of contractive-type mappings. The stability, data dependence, strong convergence, and performance of the proposed schemes are addressed. Numerical examples demonstrate that the newly introduced schemes produce approximations of great accuracy and comparable to other similar robust schemes appeared in the literature. Nevertheless, all the schemes developed here are more efficient than other robust schemes used for comparison.</p>","PeriodicalId":54709,"journal":{"name":"Numerical Algorithms","volume":null,"pages":null},"PeriodicalIF":2.1,"publicationDate":"2024-07-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"141508322","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
The forward-backward-forward algorithm with extrapolation from the past and penalty scheme for solving monotone inclusion problems and applications 解决单调包含问题的前向-后向-前向算法与过去外推法和惩罚方案及其应用
IF 2.1 3区 数学
Numerical Algorithms Pub Date : 2024-06-28 DOI: 10.1007/s11075-024-01866-0
Buris Tongnoi
{"title":"The forward-backward-forward algorithm with extrapolation from the past and penalty scheme for solving monotone inclusion problems and applications","authors":"Buris Tongnoi","doi":"10.1007/s11075-024-01866-0","DOIUrl":"https://doi.org/10.1007/s11075-024-01866-0","url":null,"abstract":"<p>In this paper, we consider an improved iterative method for solving the monotone inclusion problem in the form of <span>(0 in A(x) + D(x) + N_{C}(x))</span> in a real Hilbert space, where <i>A</i> is a maximally monotone operator, <i>D</i> and <i>B</i> are monotone and Lipschitz continuous, and <i>C</i> is the nonempty set of zeros of the operator <i>B</i>. We investigate the weak ergodic and strong convergence (when <i>A</i> is strongly monotone) of the iterates produced by our considered method. We show that the algorithmic scheme can also be applied to minimax problems. Furthermore, we discuss how to apply the method to the inclusion problem involving a finite sum of compositions of linear continuous operators by using the product space approach and employ it for convex minimization. Finally, we present a numerical experiment in TV-based image inpainting to validate the proposed theoretical theorem.</p>","PeriodicalId":54709,"journal":{"name":"Numerical Algorithms","volume":null,"pages":null},"PeriodicalIF":2.1,"publicationDate":"2024-06-28","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"141514529","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
Convergence rate and exponential stability of backward Euler method for neutral stochastic delay differential equations under generalized monotonicity conditions 广义单调性条件下中性随机延迟微分方程的后向欧拉法收敛率和指数稳定性
IF 2.1 3区 数学
Numerical Algorithms Pub Date : 2024-06-28 DOI: 10.1007/s11075-024-01862-4
Jingjing Cai, Ziheng Chen, Yuanling Niu
{"title":"Convergence rate and exponential stability of backward Euler method for neutral stochastic delay differential equations under generalized monotonicity conditions","authors":"Jingjing Cai, Ziheng Chen, Yuanling Niu","doi":"10.1007/s11075-024-01862-4","DOIUrl":"https://doi.org/10.1007/s11075-024-01862-4","url":null,"abstract":"<p>This work focuses on the numerical approximations of neutral stochastic delay differential equations with their drift and diffusion coefficients growing super-linearly with respect to both delay variables and state variables. Under generalized monotonicity conditions, we prove that the backward Euler method not only converges strongly in the mean square sense with order 1/2, but also inherit the mean square exponential stability of the original equations. As a byproduct, we obtain the same results on convergence rate and exponential stability of the backward Euler method for stochastic delay differential equations under generalized monotonicity conditions. These theoretical results are finally supported by several numerical experiments.</p>","PeriodicalId":54709,"journal":{"name":"Numerical Algorithms","volume":null,"pages":null},"PeriodicalIF":2.1,"publicationDate":"2024-06-28","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"141508312","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 fast second-order absorbing boundary condition for the linearized Benjamin-Bona-Mahony equation 线性化本杰明-博纳-马霍尼方程的快速二阶吸收边界条件
IF 2.1 3区 数学
Numerical Algorithms Pub Date : 2024-06-26 DOI: 10.1007/s11075-024-01864-2
Zijun Zheng, Gang Pang, Matthias Ehrhardt, Baiyili Liu
{"title":"A fast second-order absorbing boundary condition for the linearized Benjamin-Bona-Mahony equation","authors":"Zijun Zheng, Gang Pang, Matthias Ehrhardt, Baiyili Liu","doi":"10.1007/s11075-024-01864-2","DOIUrl":"https://doi.org/10.1007/s11075-024-01864-2","url":null,"abstract":"<p>In this paper, we present a fully discrete finite difference scheme with efficient convolution of artificial boundary conditions for solving the Cauchy problem associated with the one-dimensional linearized Benjamin-Bona-Mahony equation. The scheme utilizes the Padé expansion of the square root function in the complex plane to implement the fast convolution, resulting in significant reduction of computational costs involved in the time convolution process. Moreover, the introduction of a constant damping term in the governing equations allows for convergence analysis under specific conditions. The theoretical analysis is complemented by numerical examples that illustrate the performance of the proposed numerical method.</p>","PeriodicalId":54709,"journal":{"name":"Numerical Algorithms","volume":null,"pages":null},"PeriodicalIF":2.1,"publicationDate":"2024-06-26","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"141508316","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 reliable numerical algorithm mixed with hypergeometric function for analyzing fractional variational problems 用于分析分数变分问题的混合超几何函数的可靠数值算法
IF 2.1 3区 数学
Numerical Algorithms Pub Date : 2024-06-25 DOI: 10.1007/s11075-024-01865-1
Z. Zarvan, K. Sayevand, R. M. Ganji, H. Jafari
{"title":"A reliable numerical algorithm mixed with hypergeometric function for analyzing fractional variational problems","authors":"Z. Zarvan, K. Sayevand, R. M. Ganji, H. Jafari","doi":"10.1007/s11075-024-01865-1","DOIUrl":"https://doi.org/10.1007/s11075-024-01865-1","url":null,"abstract":"<p>The present study aims to introduce a numerical approach based on the hybrid of block-pulse functions (BPFs), Bernoulli polynomials (BPs), and hypergeometric function for analyzing a class of fractional variational problems (FVPs). The FVPs are made by the Caputo derivative sense. To analyze this problem, first, we create an approximate for the Riemann-Liouville fractional integral operator for BPFs and BPs of the fractional order. In this framework and using the Gauss-Legendre points, the main problem is converted into a system of algebraic equations. In the follow-up, an accurate upper bound is obtained and some theorems are established on the convergence analysis. Moreover, the computational order of convergence and solvability of the proposed approach are displayed and approximated theoretically and numerically. Meanwhile, the thrust of the proposed scheme is compared with other sophisticated examples in the literature, demonstrating that the process is accurate and efficient.</p>","PeriodicalId":54709,"journal":{"name":"Numerical Algorithms","volume":null,"pages":null},"PeriodicalIF":2.1,"publicationDate":"2024-06-25","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"141508317","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
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