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A note on generalized Floater–Hormann interpolation at arbitrary distributions of nodes 关于任意节点分布的广义浮子-霍尔曼插值法的说明
IF 2.1 3区 数学
Numerical Algorithms Pub Date : 2024-09-17 DOI: 10.1007/s11075-024-01933-6
Woula Themistoclakis, Marc Van Barel
{"title":"A note on generalized Floater–Hormann interpolation at arbitrary distributions of nodes","authors":"Woula Themistoclakis, Marc Van Barel","doi":"10.1007/s11075-024-01933-6","DOIUrl":"https://doi.org/10.1007/s11075-024-01933-6","url":null,"abstract":"<p>The paper is concerned with a generalization of Floater–Hormann (briefly FH) rational interpolation recently introduced by the authors. Compared with the original FH interpolants, the generalized ones depend on an additional integer parameter <span>(gamma &gt;1)</span>, that, in the limit case <span>(gamma =1)</span> returns the classical FH definition. Here we focus on the general case of an arbitrary distribution of nodes and, for any <span>(gamma &gt;1)</span>, we estimate the sup norm of the error in terms of the maximum (<i>h</i>) and minimum (<span>(h^*)</span>) distance between two consecutive nodes. In the special case of equidistant (<span>(h=h^*)</span>) or quasi–equidistant (<span>(happrox h^*)</span>) nodes, the new estimate improves previous results requiring some theoretical restrictions on <span>(gamma )</span> which are not needed as shown by the numerical tests carried out to validate the theory.</p>","PeriodicalId":54709,"journal":{"name":"Numerical Algorithms","volume":"64 1","pages":""},"PeriodicalIF":2.1,"publicationDate":"2024-09-17","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"142266837","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
An inertia projection method for nonlinear pseudo-monotone equations with convex constraints 带凸约束的非线性伪单调方程的惯性投影法
IF 2.1 3区 数学
Numerical Algorithms Pub Date : 2024-09-16 DOI: 10.1007/s11075-024-01934-5
Jinkui Liu, Ning Zhang, Bing Tang
{"title":"An inertia projection method for nonlinear pseudo-monotone equations with convex constraints","authors":"Jinkui Liu, Ning Zhang, Bing Tang","doi":"10.1007/s11075-024-01934-5","DOIUrl":"https://doi.org/10.1007/s11075-024-01934-5","url":null,"abstract":"<p>Based on DDP method proposed by Mohammad and Abubakar, in this paper we use the inertia index and relaxation factor to establish an inertia projection method for solving nonlinear pseudo-monotone equations with convex constraints. This method can generate a sufficient descent direction at each iteration, which is independent of any line search condition. Moreover, we prove the global convergence of the proposed method without assuming that the objective function satisfies the Lipschitz continuity. Numerical results demonstrate the effectiveness of the proposed method by comparing with some existing methods.</p>","PeriodicalId":54709,"journal":{"name":"Numerical Algorithms","volume":"21 1","pages":""},"PeriodicalIF":2.1,"publicationDate":"2024-09-16","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"142266838","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
Globally solving the fractional squared least squares model for GPS localization 全局求解用于 GPS 定位的分数平方最小二乘模型
IF 2.1 3区 数学
Numerical Algorithms Pub Date : 2024-09-14 DOI: 10.1007/s11075-024-01935-4
Xiaoli Cen, Yong Xia
{"title":"Globally solving the fractional squared least squares model for GPS localization","authors":"Xiaoli Cen, Yong Xia","doi":"10.1007/s11075-024-01935-4","DOIUrl":"https://doi.org/10.1007/s11075-024-01935-4","url":null,"abstract":"<p>This study presents a new branch and bound algorithm designed for the global optimization of the fractional squared least squares model for GPS localization. The algorithm incorporates a novel underestimation approach that provides theoretically superior lower bounds while requiring a comparable computational effort to the current approach. Numerical results demonstrate the substantial efficiency enhancements of the proposed algorithm over the existing algorithm.</p>","PeriodicalId":54709,"journal":{"name":"Numerical Algorithms","volume":"20 1","pages":""},"PeriodicalIF":2.1,"publicationDate":"2024-09-14","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"142266840","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
Multivariate polynomial interpolation based on Radon projections 基于拉顿投影的多变量多项式插值法
IF 2.1 3区 数学
Numerical Algorithms Pub Date : 2024-09-13 DOI: 10.1007/s11075-024-01938-1
Nguyen Anh Ngoc, Nguyen Van Khiem, Tang Van Long, Phung Van Manh
{"title":"Multivariate polynomial interpolation based on Radon projections","authors":"Nguyen Anh Ngoc, Nguyen Van Khiem, Tang Van Long, Phung Van Manh","doi":"10.1007/s11075-024-01938-1","DOIUrl":"https://doi.org/10.1007/s11075-024-01938-1","url":null,"abstract":"<p>We study multivariate polynomial interpolation based on Radon projections corresponding to the intersection of hyperplanes and the coordinate axes of <span>(mathbb {R}^n)</span>. We give a characterization of these hyperplanes which determine an interpolation polynomial uniquely. We also establish conditions such that the interpolation projectors based on Radon projections converge to the Taylor projector.</p>","PeriodicalId":54709,"journal":{"name":"Numerical Algorithms","volume":"29 1","pages":""},"PeriodicalIF":2.1,"publicationDate":"2024-09-13","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"142199656","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
Globally maximizing the ratio of two generalized quadratic matrix form functions over the Stiefel manifold 在 Stiefel 流形上最大化两个广义二次矩阵形式函数之比的全局性研究
IF 2.1 3区 数学
Numerical Algorithms Pub Date : 2024-09-13 DOI: 10.1007/s11075-024-01939-0
Longfei Wang, Yu Chen, Hongwei Jiao, Yunhai Xiao, Meijia Yang
{"title":"Globally maximizing the ratio of two generalized quadratic matrix form functions over the Stiefel manifold","authors":"Longfei Wang, Yu Chen, Hongwei Jiao, Yunhai Xiao, Meijia Yang","doi":"10.1007/s11075-024-01939-0","DOIUrl":"https://doi.org/10.1007/s11075-024-01939-0","url":null,"abstract":"<p>We consider the problem of maximizing the ratio of two generalized quadratic matrix form functions over the Stiefel manifold, i.e., <span>(max limits _{X^{T}X=I} frac{text {tr}(GX^{T}AX)}{text {tr}(GX^{T}BX)})</span> (RQMP). We utilize the Dinkelbach algorithm to globally solve RQMP, where each subproblem is evaluated by the closed-form solution. For a special case of RQMP with <span>(AB=BA)</span>, we propose an equivalent linear programming problem. Numerical experiments demonstrate that it is more efficient than the recent SDP-based algorithm.</p>","PeriodicalId":54709,"journal":{"name":"Numerical Algorithms","volume":"47 1","pages":""},"PeriodicalIF":2.1,"publicationDate":"2024-09-13","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"142199658","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
QR decomposition of dual quaternion matrix and blind watermarking scheme 双四元矩阵的 QR 分解和盲水印方案
IF 2.1 3区 数学
Numerical Algorithms Pub Date : 2024-09-13 DOI: 10.1007/s11075-024-01930-9
Mingcui Zhang, Ying Li, Tao Wang, Jianhua Sun
{"title":"QR decomposition of dual quaternion matrix and blind watermarking scheme","authors":"Mingcui Zhang, Ying Li, Tao Wang, Jianhua Sun","doi":"10.1007/s11075-024-01930-9","DOIUrl":"https://doi.org/10.1007/s11075-024-01930-9","url":null,"abstract":"<p>In this paper, the algorithms and applications of the dual quaternion QR decomposition are studied. The direct algorithm and dual structure-preserving algorithm of dual quaternion QR decomposition utilizing Householder transformation of dual quaternion vector are proposed. Numerical experiments show that two algorithms are feasible, and the dual structure-preserving algorithm is superior to the direct algorithm in terms of computational efficiency. Therefore, the dual structure-preserving algorithm of dual quaternion QR decomposition is used to color image watermarking. Experiments illustrate that our method is feasible and better than the compared methods in anti-aggression.</p>","PeriodicalId":54709,"journal":{"name":"Numerical Algorithms","volume":"7 1","pages":""},"PeriodicalIF":2.1,"publicationDate":"2024-09-13","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"142199657","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
An effective real structure-preserving algorithm for the quaternion indefinite least squares problem 四元不定最小二乘问题的有效实结构保留算法
IF 2.1 3区 数学
Numerical Algorithms Pub Date : 2024-09-12 DOI: 10.1007/s11075-024-01929-2
Zixiang Meng, Zhihan Zhou, Ying Li, Fengxia Zhang
{"title":"An effective real structure-preserving algorithm for the quaternion indefinite least squares problem","authors":"Zixiang Meng, Zhihan Zhou, Ying Li, Fengxia Zhang","doi":"10.1007/s11075-024-01929-2","DOIUrl":"https://doi.org/10.1007/s11075-024-01929-2","url":null,"abstract":"<p>This paper concentrates on the quaternion indefinite least squares (QILS) problem. Firstly, we define the quaternion J-unitary matrix and the quaternion hyperbolic Givens rotation, and study their properties. Then, based on these, we investigate the quaternion hyperbolic QR factorization, and purpose its real structure-preserving (SP) algorithm by the real representation (Q-RR) matrix of the quaternion matrix. Immediately after, we explore the solution of the QILS problem, and give a real SP algorithm of solving the QILS problem. Eventually, to illustrate the effectiveness of proposed algorithms, we offer numerical examples.</p>","PeriodicalId":54709,"journal":{"name":"Numerical Algorithms","volume":"59 1","pages":""},"PeriodicalIF":2.1,"publicationDate":"2024-09-12","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"142199668","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 trust-region framework for iteration solution of the direct INDSCAL problem in metric multidimensional scaling 度量多维标度中直接 INDSCAL 问题迭代求解的信任区域框架
IF 2.1 3区 数学
Numerical Algorithms Pub Date : 2024-09-11 DOI: 10.1007/s11075-024-01921-w
Xue-lin Zhou, Chao-qian Li
{"title":"A trust-region framework for iteration solution of the direct INDSCAL problem in metric multidimensional scaling","authors":"Xue-lin Zhou, Chao-qian Li","doi":"10.1007/s11075-024-01921-w","DOIUrl":"https://doi.org/10.1007/s11075-024-01921-w","url":null,"abstract":"<p>The well-known INdividual Differences SCALing (INDSCAL) model is intended for the simultaneous metric multidimensional scaling (MDS) of several doubly centered matrices of squared dissimilarities. An alternative approach, called for short DINDSCAL (direct INDSCAL), is proposed for analyzing directly the input matrices of squared dissimilarities. In the present work, the problem of fitting the DINDSCAL model to the data is formulated as a Riemannian optimization problem on a product matrix manifold comprised of the Stiefel sub-manifold of zero-sum matrices and non-negative diagonal matrices. A practical algorithm, based on the generic Riemannian trust-region method by Absil et al., is presented to address the underlying problem, which is characterized by global convergence and local superlinear convergence rate. Numerical experiments are conducted to illustrate the efficiency of the proposed method. Furthermore, comparisons with the existing projected gradient approach and some classical methods in the MATLAB toolbox Manopt are also provided to demonstrate the merits of the proposed approach.</p>","PeriodicalId":54709,"journal":{"name":"Numerical Algorithms","volume":"2 1","pages":""},"PeriodicalIF":2.1,"publicationDate":"2024-09-11","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"142199670","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 numerical algorithm for the computation of the noncentral beta distribution function 计算非中心贝塔分布函数的数值算法
IF 2.1 3区 数学
Numerical Algorithms Pub Date : 2024-09-10 DOI: 10.1007/s11075-024-01931-8
Vera Egorova, Amparo Gil, Javier Segura, Nico M. Temme
{"title":"A numerical algorithm for the computation of the noncentral beta distribution function","authors":"Vera Egorova, Amparo Gil, Javier Segura, Nico M. Temme","doi":"10.1007/s11075-024-01931-8","DOIUrl":"https://doi.org/10.1007/s11075-024-01931-8","url":null,"abstract":"<p>The noncentral beta distribution function is a generalization of the central beta distribution (the regularized incomplete beta function) that includes a noncentrality parameter. This paper describes an algorithm and provides a Matlab implementation for calculating the noncentral beta distribution function. Through a series of numerical tests, we demonstrate that the algorithm is accurate and efficient across a wide range of parameters.</p>","PeriodicalId":54709,"journal":{"name":"Numerical Algorithms","volume":"15 1","pages":""},"PeriodicalIF":2.1,"publicationDate":"2024-09-10","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"142199660","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 algorithms for recovering a fractional Sturm-Liouville operator based on trace formulae 基于迹公式的分数斯特姆-利乌维尔算子恢复数值算法
IF 2.1 3区 数学
Numerical Algorithms Pub Date : 2024-09-07 DOI: 10.1007/s11075-024-01926-5
Xiaowen Li, Xiaoying Jiang, Xiang Xu
{"title":"Numerical algorithms for recovering a fractional Sturm-Liouville operator based on trace formulae","authors":"Xiaowen Li, Xiaoying Jiang, Xiang Xu","doi":"10.1007/s11075-024-01926-5","DOIUrl":"https://doi.org/10.1007/s11075-024-01926-5","url":null,"abstract":"<p>This paper explores numerical methods for recovering a density term in a fractional Sturm-Liouville problem using a set of spectra. By applying Lidskii’s theorem, a sequence of trace formulae are derived to elucidate the connections between the unknown coefficients and the complex eigenvalues of a fractional spectra problem. Two efficient algorithms are proposed based on these trace formulae, and their effectiveness is demonstrated through numerical experiments.</p>","PeriodicalId":54709,"journal":{"name":"Numerical Algorithms","volume":"6 1","pages":""},"PeriodicalIF":2.1,"publicationDate":"2024-09-07","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"142199659","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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