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A Novel Iterative Method to Find theMoore-Penrose Inverse of a Tensor with Einstein Product

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Numerical Mathematics(Theory,Methods and Applications) 2024年第1期17卷 37-68页

作者： Raziyeh Erfanifar Masoud Hajarian Khosro Sayevand department of Applied Mathematics Faculty of Mathematical SciencesShahid Beheshti UniversityTehranIran faculty of Mathematics and statistics Malayer UniversityMalayerIran

In this study,based on an iterative method to solve nonlinear equations,a third-order convergent iterative method to compute the Moore-Penrose inverse of a tensor with the Einstein product is presented and *** compar-isons of the proposed method with other methods show that the average number of iterations,number of the Einstein products,and CPU time of our method are considerably less than other *** some applications,partial and fractional differential equations that lead to sparse matrices are considered as *** use the iterates obtained by the method as a preconditioner,based on tensor form to solve the multilinear system A∗N X=***,several practical numerical examples are also given to display the accuracy and efﬁciency of the new *** presented results show that the proposed method is very robust for obtaining the Moore-Penrose inverse of tensors.

关键词： Tensor iterative methods Moore-Penrose inverse Einstein product

On Polar Decomposition of Tensors with Einstein Product and a Novel Iterative Parametric Method

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Numerical Mathematics(Theory,Methods and Applications) 2024年第1期17卷 69-92页

This study aims to investigate the polar decomposition of tensors with the Einstein product for theﬁrst *** polar decomposition of tensors can be computed using the singular value decomposition of the tensors with the Einstein *** the following,some iterative methods forﬁnding the polar decomposi-tion of matrices have been developed into iterative methods to compute the polar decomposition of ***,we propose a novel parametric iterative method toﬁnd the polar decomposition of *** the obtained conditions,we prove that the proposed parametric method has the order of convergence *** every iteration of the proposed method,only four Einstein products are required,while other iterative methods need to calculate multiple Einstein products and one tensor inversion in each ***,the new method is superior in terms of efﬁciency ***,the numerical comparisons performed among several well-known methods,show that the proposed method is remarkably efﬁcient and accurate.

关键词： Iterative methods Einstein product polar decomposition of a tensor polar factor order of convergence

Bifurcation Analysis of a Nonlinear Vibro-Impact System with an Uncertain Parameter via OPA Method

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工程与科学中的计算机建模(英文) 2024年第1期138卷 509-524页

作者： Dongmei Huang Dang Hong Wei Li Guidong Yang Vesna Rajic School of Mathematics and statistics Xidian UniversityXi’an710071China department of Mathematics Changzhi UniversityChangzhi046011China department for statistics and Mathematics Faculty of EconomicsUniversity of BelgradeBelgrade11000Serbia

In this paper,the bifurcation properties of the vibro-impact systems with an uncertain parameter under the impulse and harmonic excitations are ***,by means of the orthogonal polynomial approximation(OPA)method,the nonlinear damping and stiffness are expanded into the linear combination of the state *** condition for the appearance of the vibro-impact phenomenon is to be transformed based on the calculation of themean ***,the stochastic vibro-impact systemcan be turned into an equivalent high-dimensional deterministic non-smooth *** different Poincarésections are chosen to analyze the bifurcation properties and the impact numbers are identified for the periodic ***,the numerical results verify the effectiveness of the approximation method for analyzing the considered nonlinear ***,the bifurcation properties of the system with an uncertain parameter are explored through the high-dimensional deterministic *** can be found that the excitation frequency can induce period-doubling bifurcation and grazing *** the randomintensitymay result in a diffusion-based trajectory and the impact with the constraint plane,which induces the topological behavior of the non-smooth system to change *** is also found that grazing bifurcation appears in advance with increasing of the random *** stronger impulse force can result in the appearance of the diffusion phenomenon.

关键词： Orthogonal polynomial approximation vibro-impact systems non-smooth systems grazing bifurcation

Optimal Model Average Prediction in Orthogonal Kriging Models

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Journal of Systems Science & Complexity 2024年第3期37卷 1080-1099页

作者： WANG Jun HE Jiabei LIANG Hua LI Xinmin School of Mathematics and statistics Qingdao UniversityQingdao 266071China department of statistics George Washington UniversityWashington DC 20052USA

The main objective of this paper is to consider model averaging methods for kriging *** paper proposes a Mallows model averaging procedure for the orthogonal kriging model and demonstrate the asymptotic optimality of the model averaging estimators in terms of mean square *** studies are conducted to evaluate the performance of the proposed method and compare it with the competitors to demonstrate its *** authors also analyse a real dataset for an illustration.

关键词： Asymptotic optimality Mallows criterion optimal model averaging orthogonal kriging model

Character Sheaves for Classical Graded Lie Algebras

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Acta Mathematica Sinica,English Series 2024年第3期40卷 870-884页

作者： Ting XUE School of Mathematics and statistics University of MelbourneVIC 3010Australia department of Mathematics and statistics University of HelsinkiHelsinki 00014Finland

In this note we study character sheaves for graded Lie algebras arising from inner automorphisms of special linear groups and Vinberg’s type Ⅱ classical graded Lie algebras.

关键词： Graded Lie algebras character sheaves Fourier transform nilpotent orbits

A STABILITY RESULT FOR TRANSLATINGSPACELIKE GRAPHS IN LORENTZ MANIFOLDS

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Acta Mathematica Scientia 2024年第2期44卷 474-483页

作者：高雅毛井吴传喜 faculty of Mathematics and statistics Key Laboratory of Applied Mathematics of Hubei ProvinceHubei UniversityWuhan430062China

In this paper,we investigate spacelike graphs defined over a domain Ω⊂M^(n) in the Lorentz manifold M^(n)×ℝ with the metric−ds^(2)+σ,where M^(n) is a complete Riemannian n-manifold with the metricσ,Ωhas piecewise smooth boundary,and ℝ denotes the Euclidean *** prove an interesting stability result for translating spacelike graphs in M^(n)×ℝ under a conformal transformation.

关键词： mean curvature flow spacelike graphs translating spacelike graphs maximal spacelike graphs constant mean curvature Lorentz manifolds

Double Moving Extremes Ranked Set Sampling Design

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Acta Mathematicae Applicatae Sinica 2024年第1期40卷 75-90页

作者： Meng Chen Wang-xue Chen Rui Yang department of Mathematics and statistics Jishou UniversityJishou416000China

The traditional simple random sampling(SRS)design method is inefficient in many *** proposed some new designs to increase *** this paper,as a variation of moving extremes ranked set sampling(MERSS),double MERSS(DMERSS)is proposed and its properties for estimating the population mean are *** turns out that,when the underlying distribution is symmetric,DMERSS gives unbiased estimators of the population ***,it is found that DMERSS is more efficient than the SRS and MERSS methods for usual symmetric distributions(normal and uniform).For asymmetric distributions considered in this study,the DMERSS has a small bias and it is more efficient than SRS for usual asymmetric distribution(exponential)for small sample sizes.

关键词： double moving extremes ranked set sampling symmetric distribution efficiency

Computational Analysis of Novel Extended Lindley Progressively Censored Data

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Computer Modeling in Engineering & Sciences 2024年第3期138卷 2571-2596页

作者： Refah Alotaibi Mazen Nassar Ahmed Elshahhat department of Mathematical Sciences College of SciencePrincess Nourah bint Abdulrahman UniversityP.O.Box 84428Riyadh11671Saudi Arabia department of statistics Faculty of ScienceKing Abdulaziz UniversityJeddah21589Saudi Arabia department of statistics Faculty of CommerceZagazig UniversityZagazigEgypt faculty of Technology and Development Zagazig UniversityZagazig44519Egypt

A novel extended Lindley lifetime model that exhibits unimodal or decreasing density shapes as well as increasing,bathtub or unimodal-then-bathtub failure rates, named the Marshall-Olkin-Lindley (MOL) model is *** this research, using a progressive Type-II censored, various inferences of the MOL model parameters oflife are introduced. Utilizing the maximum likelihood method as a classical approach, the estimators of themodel parameters and various reliability measures are investigated. Against both symmetric and asymmetric lossfunctions, the Bayesian estimates are obtained using the Markov Chain Monte Carlo (MCMC) technique with theassumption of independent gamma priors. From the Fisher information data and the simulatedMarkovian chains,the approximate asymptotic interval and the highest posterior density interval, respectively, of each unknownparameter are calculated. Via an extensive simulated study, the usefulness of the various suggested strategies isassessedwith respect to some evaluationmetrics such as mean squared errors, mean relative absolute biases, averageconfidence lengths, and coverage percentages. Comparing the Bayesian estimations based on the asymmetric lossfunction to the traditional technique or the symmetric loss function-based Bayesian estimations, the analysisdemonstrates that asymmetric loss function-based Bayesian estimations are preferred. Finally, two data sets,representing vinyl chloride and repairable mechanical equipment items, have been investigated to support theapproaches proposed and show the superiority of the proposed model compared to the other fourteen lifetimemodels.

关键词： Marshall-Olkin-Lindleymodel reliability inference Bayesian and classical inference progressive Type-II censoring

Berry-Esseen bounds for self-normalized sums of locally dependent random variables

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Science China Mathematics 2024年第11期67卷 2629-2652页

作者： Zhuo-Song Zhang department of statistics and Data Science Southern University of Science and Technology

The Berry-Esseen bound provides an upper bound on the Kolmogorov distance between a random variable and the normal *** this paper,we establish Berry-Esseen bounds with optimal rates for self-normalized sums of locally dependent random variables,assuming only a second-moment *** proof leverages Stein's method and introduces a novel randomized concentration inequality,which may also be of independent interest for other *** main results have applied to self-normalized sums of m-dependent random variables and graph dependency models.

关键词： Berry-Esseen bounds self-normalized sums localdependence $m$-dependence graph dependency