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Variable parameter Uzawa method for solving the indefinite least squares problem 求解不定最小二乘法问题的可变参数乌泽法
IF 2.1 3区 数学
Numerical Algorithms Pub Date : 2024-07-31 DOI: 10.1007/s11075-024-01905-w
Lingsheng Meng, Kailiang Xin, Jun Li
{"title":"Variable parameter Uzawa method for solving the indefinite least squares problem","authors":"Lingsheng Meng, Kailiang Xin, Jun Li","doi":"10.1007/s11075-024-01905-w","DOIUrl":"https://doi.org/10.1007/s11075-024-01905-w","url":null,"abstract":"<p>In this paper, the variable parameter Uzawa method is presented to solve the indefinite least squares problem. The proposed iterative method is unconditionally convergent, and its iterative algorithm and parameter designing are simple and efficient. Numerical experiments show that the variable parameter Uzawa method is superior to the USSOR method (Song, Int. J. Comput. Math. <b>97</b>, 1781–1791 2020) and the splitting-based randomized iterative method (Zhang and Li, Appl. Math. Comput. <b>446</b>, 127892 2023).</p>","PeriodicalId":54709,"journal":{"name":"Numerical Algorithms","volume":"75 1","pages":""},"PeriodicalIF":2.1,"publicationDate":"2024-07-31","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"141870101","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
Refined and refined harmonic Jacobi–Davidson methods for computing several GSVD components of a large regular matrix pair 计算大型正则矩阵对的多个 GSVD 分量的改进和改进谐波雅各比-戴维森方法
IF 2.1 3区 数学
Numerical Algorithms Pub Date : 2024-07-31 DOI: 10.1007/s11075-024-01901-0
Jinzhi Huang, Zhongxiao Jia
{"title":"Refined and refined harmonic Jacobi–Davidson methods for computing several GSVD components of a large regular matrix pair","authors":"Jinzhi Huang, Zhongxiao Jia","doi":"10.1007/s11075-024-01901-0","DOIUrl":"https://doi.org/10.1007/s11075-024-01901-0","url":null,"abstract":"<p>Three refined and refined harmonic extraction-based Jacobi–Davidson (JD) type methods are proposed, and their thick-restart algorithms with deflation and purgation are developed to compute several generalized singular value decomposition (GSVD) components of a large regular matrix pair. The new methods are called refined cross product-free (RCPF), refined cross product-free harmonic (RCPF-harmonic) and refined inverse-free harmonic (RIF-harmonic) JDGSVD algorithms, abbreviated as RCPF-JDGSVD, RCPF-HJDGSVD and RIF-HJDGSVD, respectively. The new JDGSVD methods are more efficient than the corresponding standard and harmonic extraction-based JDSVD methods proposed previously by the authors, and can overcome the erratic behavior and intrinsic possible non-convergence of the latter ones. Numerical experiments illustrate that RCPF-JDGSVD performs better for the computation of extreme GSVD components while RCPF-HJDGSVD and RIF-HJDGSVD are more suitable for that of interior GSVD components.</p>","PeriodicalId":54709,"journal":{"name":"Numerical Algorithms","volume":"49 1","pages":""},"PeriodicalIF":2.1,"publicationDate":"2024-07-31","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"141873268","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 Tikhonov-type regularization method for Caputo fractional derivative 卡普托分数导数的提霍诺夫式正则化方法
IF 2.1 3区 数学
Numerical Algorithms Pub Date : 2024-07-30 DOI: 10.1007/s11075-024-01883-z
Nguyen Van Duc, Thi-Phong Nguyen, Nguyen Phuong Ha, Nguyen The Anh, Luu Duc Manh, Hoang Cong Gia Bao
{"title":"A Tikhonov-type regularization method for Caputo fractional derivative","authors":"Nguyen Van Duc, Thi-Phong Nguyen, Nguyen Phuong Ha, Nguyen The Anh, Luu Duc Manh, Hoang Cong Gia Bao","doi":"10.1007/s11075-024-01883-z","DOIUrl":"https://doi.org/10.1007/s11075-024-01883-z","url":null,"abstract":"<p>Stability estimates of Hölder type for the problem of evaluating the Caputo fractional derivative are obtained. This ill-posed problem is regularized by a Tikhonov-type method, which guarantees error estimates of Hölder type. Numerical results are presented to confirm the theory.</p>","PeriodicalId":54709,"journal":{"name":"Numerical Algorithms","volume":"44 1","pages":""},"PeriodicalIF":2.1,"publicationDate":"2024-07-30","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"141870100","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
Generalized weak Galerkin finite element method for linear elasticity interface problems 线性弹性界面问题的广义弱 Galerkin 有限元方法
IF 2.1 3区 数学
Numerical Algorithms Pub Date : 2024-07-29 DOI: 10.1007/s11075-024-01904-x
Yue Wang, Fuzheng Gao
{"title":"Generalized weak Galerkin finite element method for linear elasticity interface problems","authors":"Yue Wang, Fuzheng Gao","doi":"10.1007/s11075-024-01904-x","DOIUrl":"https://doi.org/10.1007/s11075-024-01904-x","url":null,"abstract":"<p>A generalized weak Galerkin finite element method for linear elasticity interface problems is presented. The generalized weak gradient (divergence) is consisted of classical gradient (divergence) and the solution of local problem. Thus, the finite element space can be extended to arbitrary combination of piecewise polynomial spaces. The error equation and error estimates are proved. The numerical results illustrate the efficiency and flexibility for different interfaces, partitions and combinations, the locking-free property, the well performance for low regularity solution in discrete energy, <span>(L^2)</span> and <span>(L^{infty })</span> norms. Meanwhile, we present the numerical comparison between our algorithm and the weak Galerkin finite element algorithm to demonstrate the flexibility of our algorithm. In addition, for some cases, the convergence rates in numerical tests are obviously higher than the theoretical prediction for the smooth and low regularity solutions.</p>","PeriodicalId":54709,"journal":{"name":"Numerical Algorithms","volume":"44 1","pages":""},"PeriodicalIF":2.1,"publicationDate":"2024-07-29","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"141870102","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
Extended explicit Pseudo two-step Runge-Kutta-Nyström methods for general second-order oscillatory systems 一般二阶振荡系统的扩展显式伪两步 Runge-Kutta-Nyström 方法
IF 2.1 3区 数学
Numerical Algorithms Pub Date : 2024-07-29 DOI: 10.1007/s11075-024-01896-8
Yonglei Fang, Changying Liu, Xiong You
{"title":"Extended explicit Pseudo two-step Runge-Kutta-Nyström methods for general second-order oscillatory systems","authors":"Yonglei Fang, Changying Liu, Xiong You","doi":"10.1007/s11075-024-01896-8","DOIUrl":"https://doi.org/10.1007/s11075-024-01896-8","url":null,"abstract":"<p>Explicit pseudo two-step extended Runge-Kutta-Nyström (EPTSERKN) methods for the numerical integration of general second-order oscillatory differential systems are discussed in this paper. New explicit pseudo two-step Runge-Kutta-Nyström (EPTSRKN) methods and explicit extended Runge-Kutta-Nyström (ERKN) methods are derived. We give the global error analysis of the new methods. The <i>s</i>-stages new methods are of order <span>(s+1)</span> with some suitable nodes. Numerical experiments are carried out to show the efficiency and robustness of the new methods.</p>","PeriodicalId":54709,"journal":{"name":"Numerical Algorithms","volume":"2 1","pages":""},"PeriodicalIF":2.1,"publicationDate":"2024-07-29","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"141870104","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
Fast and accurate numerical algorithm for solving stochastic Itô-Volterra integral equations 求解随机伊托-伏特拉积分方程的快速准确数值算法
IF 2.1 3区 数学
Numerical Algorithms Pub Date : 2024-07-29 DOI: 10.1007/s11075-024-01898-6
Rebiha Zeghdane
{"title":"Fast and accurate numerical algorithm for solving stochastic Itô-Volterra integral equations","authors":"Rebiha Zeghdane","doi":"10.1007/s11075-024-01898-6","DOIUrl":"https://doi.org/10.1007/s11075-024-01898-6","url":null,"abstract":"<p>The purpose of this paper is to present a simple numerical technique for approximating the solutions of stochastic Volterra integral equations. The proposed method depends on the Picard iteration and uses a suitable quadrature rule. Error estimates and associated theorems have been proved for this proposed technique. Some test examples have been studied to verify the applicability and accuracy of the proposed technique.</p>","PeriodicalId":54709,"journal":{"name":"Numerical Algorithms","volume":"80 1","pages":""},"PeriodicalIF":2.1,"publicationDate":"2024-07-29","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"141870112","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
Limited memory gradient methods for unconstrained optimization 无约束优化的有限记忆梯度法
IF 2.1 3区 数学
Numerical Algorithms Pub Date : 2024-07-26 DOI: 10.1007/s11075-024-01895-9
Giulia Ferrandi, Michiel E. Hochstenbach
{"title":"Limited memory gradient methods for unconstrained optimization","authors":"Giulia Ferrandi, Michiel E. Hochstenbach","doi":"10.1007/s11075-024-01895-9","DOIUrl":"https://doi.org/10.1007/s11075-024-01895-9","url":null,"abstract":"<p>The limited memory steepest descent method (LMSD, Fletcher, 2012) for unconstrained optimization problems stores a few past gradients to compute multiple stepsizes at once. We review this method and propose new variants. For strictly convex quadratic objective functions, we study the numerical behavior of different techniques to compute new stepsizes. In particular, we introduce a method to improve the use of harmonic Ritz values. We also show the existence of a secant condition associated with LMSD, where the approximating Hessian is projected onto a low-dimensional space. In the general nonlinear case, we propose two new alternatives to Fletcher’s method: first, the addition of symmetry constraints to the secant condition valid for the quadratic case; second, a perturbation of the last differences between consecutive gradients, to satisfy multiple secant equations simultaneously. We show that Fletcher’s method can also be interpreted from this viewpoint.</p>","PeriodicalId":54709,"journal":{"name":"Numerical Algorithms","volume":"51 1","pages":""},"PeriodicalIF":2.1,"publicationDate":"2024-07-26","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"141785244","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
Computation of polynomial and rational approximations in complex domains by the $$tau $$ -method 用 $$tau$ 方法计算复域中的多项式和有理近似值
IF 2.1 3区 数学
Numerical Algorithms Pub Date : 2024-07-25 DOI: 10.1007/s11075-024-01897-7
Irina Georgieva, Clemens Hofreither
{"title":"Computation of polynomial and rational approximations in complex domains by the $$tau $$ -method","authors":"Irina Georgieva, Clemens Hofreither","doi":"10.1007/s11075-024-01897-7","DOIUrl":"https://doi.org/10.1007/s11075-024-01897-7","url":null,"abstract":"<p>We investigate numerical methods for computation of polynomial and rational approximations of functions in complex domains based on Faber polynomials and the Lanczos <span>(tau )</span>-method. Our interest is motivated by applications in fractional partial differential equations. We give an overview of previous results related to the basis of Faber polynomials associated with a complex domain, Faber expansion, and the Lanczos <span>(tau )</span>-method. We also collect numerical algorithms for the computational realization of these concepts. Our main new contribution is a <span>(tau )</span>-method for rational approximation in complex domains which uses Faber polynomials in the perturbation term. We realize it via a novel hybrid symbolic-numeric algorithm which can be applied to arbitrary functions satisfying a suitable differential equation. We present some numerical examples, where we use sectors lying in the complex plane as our domains of interest. We compare results for the various polynomial and rational approximation techniques outlined above; in particular, we observe exponential convergence with respect to the rational degree for our proposed method.</p>","PeriodicalId":54709,"journal":{"name":"Numerical Algorithms","volume":"15 1","pages":""},"PeriodicalIF":2.1,"publicationDate":"2024-07-25","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"141775194","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
Unified convergence analysis of a class of iterative methods 一类迭代法的统一收敛分析
IF 2.1 3区 数学
Numerical Algorithms Pub Date : 2024-07-24 DOI: 10.1007/s11075-024-01893-x
Muniyasamy M, Santhosh George, Chandhini G
{"title":"Unified convergence analysis of a class of iterative methods","authors":"Muniyasamy M, Santhosh George, Chandhini G","doi":"10.1007/s11075-024-01893-x","DOIUrl":"https://doi.org/10.1007/s11075-024-01893-x","url":null,"abstract":"<p>In this paper, unified convergence analyses for a class of iterative methods of order three, five, and six are studied to solve the nonlinear systems in Banach space settings. Our analysis gives the number of iterations needed to achieve the given accuracy and the radius of the convergence ball precisely using weaker conditions on the involved operator. Various numerical examples have been taken to illustrate the proposed method, and the theoretical convergence has been validated via these examples.</p>","PeriodicalId":54709,"journal":{"name":"Numerical Algorithms","volume":"68 1","pages":""},"PeriodicalIF":2.1,"publicationDate":"2024-07-24","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"141775195","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 solving a revised model of the nonnegative matrix factorization problem by the modified adaptive versions of the Dai–Liao method 关于用戴廖法的修正自适应版本求解非负矩阵因式分解问题的修正模型
IF 2.1 3区 数学
Numerical Algorithms Pub Date : 2024-07-24 DOI: 10.1007/s11075-024-01886-w
Saman Babaie-Kafaki, Fatemeh Dargahi, Zohre Aminifard
{"title":"On solving a revised model of the nonnegative matrix factorization problem by the modified adaptive versions of the Dai–Liao method","authors":"Saman Babaie-Kafaki, Fatemeh Dargahi, Zohre Aminifard","doi":"10.1007/s11075-024-01886-w","DOIUrl":"https://doi.org/10.1007/s11075-024-01886-w","url":null,"abstract":"<p>We suggest a revised form of a classic measure function to be employed in the optimization model of the nonnegative matrix factorization problem. More exactly, using sparse matrix approximations, the revision term is embedded to the model for penalizing the ill-conditioning in the computational trajectory to obtain the factorization elements. Then, as an extension of the Euclidean norm, we employ the ellipsoid norm to gain adaptive formulas for the Dai–Liao parameter in a least-squares framework. In essence, the parametric choices here are obtained by pushing the Dai–Liao direction to the direction of a well-functioning three-term conjugate gradient algorithm. In our scheme, the well-known BFGS and DFP quasi–Newton updating formulas are used to characterize the positive definite matrix factor of the ellipsoid norm. To see at what level our model revisions as well as our algorithmic modifications are effective, we seek some numerical evidence by conducting classic computational tests and assessing the outputs as well. As reported, the results weigh enough value on our analytical efforts.</p>","PeriodicalId":54709,"journal":{"name":"Numerical Algorithms","volume":"72 1","pages":""},"PeriodicalIF":2.1,"publicationDate":"2024-07-24","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"141775192","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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