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A note on the Moore-Penrose inverse of a companion matrix
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作者 王龙 陈建龙 《Journal of Southeast University(English Edition)》 EI CAS 2017年第1期123-126,共4页
Let R be an associative ring with unity 1. The existence of the Moore-Penrose inverses of block matrices overR is investigated and the sufficient ad necessary conditions for such existence are obtained. Furthermore, ... Let R be an associative ring with unity 1. The existence of the Moore-Penrose inverses of block matrices overR is investigated and the sufficient ad necessary conditions for such existence are obtained. Furthermore, the representation of the Moore-Penrose inverse of M=[0 A C B]is given under the condition of EBF - 0, where E - I - CCT and F - I -AfA. This result generalizes the representation of the Moore-Penrose inverse of the companion matrix M =[0 a In b]due to Pedro Patricio. As for applications, some examples are given to illustrate the obtained results. 展开更多
关键词 companion matrix moore-penrose inverse RING
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The Reverse Order Law for Moore-Penrose Inverse of Closed Operators 被引量:3
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作者 DU Fa-peng XUE Yi-feng 《Chinese Quarterly Journal of Mathematics》 CSCD 2013年第1期139-146,共8页
In this paper, the reverse order law for the Moore-Penrose inverse of closed linear operators with closed range is investigated by virtue of the Norm-preserving extension of the bounded linear operators. The results g... In this paper, the reverse order law for the Moore-Penrose inverse of closed linear operators with closed range is investigated by virtue of the Norm-preserving extension of the bounded linear operators. The results generalize some results obtained by S Izumino in [12]. 展开更多
关键词 reverse order law norm-preserving extension moore-penrose inverse
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Unified Approach to the Expression for the Moore-Penrose Inverse of a- xy 被引量:1
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作者 D U Fa-peng XUE Yi-feng 《Chinese Quarterly Journal of Mathematics》 CSCD 2014年第3期465-474,共10页
Let A be an unital C*-algebra, a, x and y are elements in A. In this paper, we present a method how to calculate the Moore-Penrose inverse of a- xy*and investigate the expression for some new special cases of(a- xy*).
关键词 C*-algebra generalized inverse moore-penrose inverse
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Moore-Penrose Inverses and Group Inverses of Block k-Circulant Matrices 被引量:1
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作者 Chen Jianlong(Department of Mathematics and Mechanics, Southeast University, Naming, 210018) 《Chinese Quarterly Journal of Mathematics》 CSCD 1996年第1期86-99,共14页
The Moore-Penrose inverse of a block k-circulant matrix whose blocks are arbitrary matrices are obtained when k has unit modulus. In the meantime. explicit formulae for finding group inverses of certain specified k-ci... The Moore-Penrose inverse of a block k-circulant matrix whose blocks are arbitrary matrices are obtained when k has unit modulus. In the meantime. explicit formulae for finding group inverses of certain specified k-circulant matrices are also given. 展开更多
关键词 moore-penrose inverse group inverse block k-circulant matrix
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Perturbation Analysis for t-Product-Based Tensor Inverse,Moore-Penrose Inverse and Tensor System
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作者 Zhengbang Cao Pengpeng Xie 《Communications on Applied Mathematics and Computation》 2022年第4期1441-1456,共16页
This paper establishes some perturbation analysis for the tensor inverse,the tensor Moore-Penrose inverse,and the tensor system based on the t-product.In the settings of structured perturbations,we generalize the Sher... This paper establishes some perturbation analysis for the tensor inverse,the tensor Moore-Penrose inverse,and the tensor system based on the t-product.In the settings of structured perturbations,we generalize the Sherman-Morrison-Woodbury(SMW)formula to the t-product tensor scenarios.The SMW formula can be used to perform the sensitivity analy-sis for a multilinear system of equations. 展开更多
关键词 Perturbation analysis moore-penrose inverse tensor inverse Multilinear system Sherman-Morrison-Woodbury(SMW)formula
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Computing the Moore-Penrose Inverse of a Matrix Through Symmetric Rank-One Updates 被引量:1
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作者 Xuzhou Chen Jun Ji 《American Journal of Computational Mathematics》 2011年第3期147-151,共5页
This paper presents a recursive procedure to compute the Moore-Penrose inverse of a matrix A. The method is based on the expression for the Moore-Penrose inverse of rank-one modified matrix. The computational complexi... This paper presents a recursive procedure to compute the Moore-Penrose inverse of a matrix A. The method is based on the expression for the Moore-Penrose inverse of rank-one modified matrix. The computational complexity of the method is analyzed and a numerical example is included. A variant of the algorithm with lower computational complexity is also proposed. Both algorithms are tested on randomly generated matrices. Numerical performance confirms our theoretic results. 展开更多
关键词 FINITE RECURSIVE Algorithm moore-penrose inverse SYMMETRIC Rank-One UPDATE
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Moore-Penrose Inverse and Semilinear Equations
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作者 Hugo Leiva Raúl Manzanilla 《Advances in Linear Algebra & Matrix Theory》 2018年第1期11-17,共7页
In this paper, we study the existence of solutions for the semilinear equation , where A is a , , and is a nonlinear continuous function. Assuming that the Moore-Penrose inverse AT(AAT)-1?exists (A denotes the transpo... In this paper, we study the existence of solutions for the semilinear equation , where A is a , , and is a nonlinear continuous function. Assuming that the Moore-Penrose inverse AT(AAT)-1?exists (A denotes the transposed matrix of A) which is true whenever the determinant of the matrix AAT is different than zero, and the following condition on the nonlinear term satisfied . We prove that the semilinear equation has solutions for all. Moreover, these solutions can be found from the following fixed point relation . 展开更多
关键词 SEMILINEAR EQUATIONS moore-penrose inverse Rothe’s Fixed POINT THEOREM
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Approximation Theorems of Moore-Penrose Inverse by Outer Inverses
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作者 Qianglian Huang Zheng Fang 《Numerical Mathematics A Journal of Chinese Universities(English Series)》 SCIE 2006年第2期113-119,共7页
Let X and Y be Hilbert spaces and T a bounded linear operator from X into Y with a separable range. In this note, we prove, without assuming the closeness of the range of T , that the Moore-Penrose inverse T + of T ca... Let X and Y be Hilbert spaces and T a bounded linear operator from X into Y with a separable range. In this note, we prove, without assuming the closeness of the range of T , that the Moore-Penrose inverse T + of T can be approximated by its bounded outer inverses T n# with finite ranks. 展开更多
关键词 近似定理 希尔伯特空间 摩尔-彭罗斯逆 外逆 有界线性算子 可分值域
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A Novel Iterative Method to Find the Moore-Penrose Inverse of a Tensor with Einstein Product
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作者 Raziyeh Erfanifar Masoud Hajarian Khosro Sayevand 《Numerical Mathematics(Theory,Methods and Applications)》 SCIE CSCD 2024年第1期37-68,共32页
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 analyzed.Nu... 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 analyzed.Numerical 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 methods.In some applications,partial and fractional differential equations that lead to sparse matrices are considered as prototypes.We use the iterates obtained by the method as a preconditioner,based on tensor form to solve the multilinear system A∗N X=B.Finally,several practical numerical examples are also given to display the accuracy and efficiency of the new method.The presented results show that the proposed method is very robust for obtaining the Moore-Penrose inverse of tensors. 展开更多
关键词 TENSOR iterative methods moore-penrose inverse Einstein product
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New Identities for Moore-Penrose Inverses of Some Operator Products and Their Reverse-order Laws
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作者 Mehdi MOHAMMADZADEH KARIZAKI Javad FAROKHI-OSTAD 《Acta Mathematica Sinica,English Series》 SCIE CSCD 2023年第12期2414-2426,共13页
We establish new identities for Moore-Penrose inverses of some operator products,and prove their associated reverse-order laws.Moreover,our results concerning the Moore-Penrose inverse of a product of two operators le... We establish new identities for Moore-Penrose inverses of some operator products,and prove their associated reverse-order laws.Moreover,our results concerning the Moore-Penrose inverse of a product of two operators lead in finding a relation between the operators in the case where Greville's inclusions are made into equalities. 展开更多
关键词 moore-penrose inverse Reverse-order Law
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Weighted Moore-Penrose inverses and fundamental theorem of even-order tensors with Einstein product 被引量:10
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作者 Jun JI Yimin WEI 《Frontiers of Mathematics in China》 SCIE CSCD 2017年第6期1319-1337,共19页
We treat even-order tensors with Einstein product as linear operators from tensor space to tensor space, define the mill spaces and the ranges of tensors, and study their relationship. We extend the fundamental theore... We treat even-order tensors with Einstein product as linear operators from tensor space to tensor space, define the mill spaces and the ranges of tensors, and study their relationship. We extend the fundamental theorem of linear algebra for matrix spaces to tensor spaces. Using the new relationship, we characterize the least-squares (M) solutions to a multilineax system and establish the relationship between the minimum-norm (N) leastsquares (M)solution of a multilinear system and the weighted Moore-Penrose inverse of its coefficient tensor. We also investigate a class of even-order tensors induced by matrices and obtain some interesting properties. 展开更多
关键词 Fundamental theorem weighted moore-penrose inverse multi- linear system null space and range tensor equation
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Weighted Moore-Penrose Inverses and Weighted Core Inverses in Rings with Involution 被引量:2
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作者 Huihui ZHU Qing-Wen WANG 《Chinese Annals of Mathematics,Series B》 SCIE CSCD 2021年第4期613-624,共12页
In this paper,the authors derive the existence criteria and the formulae of the weighted Moore-Penrose inverse,the e-core inverse and the f-dual core inverse in rings.Also,new characterizations between weighted Moore-... In this paper,the authors derive the existence criteria and the formulae of the weighted Moore-Penrose inverse,the e-core inverse and the f-dual core inverse in rings.Also,new characterizations between weighted Moore-Penrose inverses and one-sided inverses along an element are given. 展开更多
关键词 Weighted moore-penrose inverses One-sided inverses along an element inverses along an element e-Core inverses f-Dual core inverses
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Inverse design of mechanical metamaterial achieving a prescribedconstitutive curve 被引量:1
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作者 Zongliang Du Tanghuai Bian +4 位作者 Xiaoqiang Ren Yibo Jia Shan Tang Tianchen Cui Xu Guo 《Theoretical & Applied Mechanics Letters》 CAS CSCD 2024年第1期16-22,共7页
Besides exhibiting excellent capabilities such as energy absorption,phase-transforming metamaterials offer a vast design space for achieving nonlinear constitutive relations.This is facilitated by switching between di... Besides exhibiting excellent capabilities such as energy absorption,phase-transforming metamaterials offer a vast design space for achieving nonlinear constitutive relations.This is facilitated by switching between different patterns under deformation.However,the related inverse design problem is quite challenging,due to the lack of appropriate mathematical formulation and the convergence issue in the post-buckling analysis of intermediate designs.In this work,periodic unit cells are explicitly described by the moving morphable voids method and effectively analyzed by eliminating the degrees of freedom in void regions.Furthermore,by exploring the Pareto frontiers between error and cost,an inverse design formulation is proposed for unit cells.This formulation aims to achieve a prescribed constitutive curve and is validated through numerical examples and experimental results.The design approach presented here can be extended to the inverse design of other types of mechanical metamaterials with prescribed nonlinear effective properties. 展开更多
关键词 METAMATERIAL Pattern-transformation Constitutive curve inverse design
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OptoGPT: A foundation model for inverse design in optical multilayer thin film structures 被引量:1
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作者 Taigao Ma Haozhu Wang L.Jay Guo 《Opto-Electronic Advances》 SCIE EI CAS CSCD 2024年第7期4-16,共13页
Optical multilayer thin film structures have been widely used in numerous photonic applications.However,existing inverse design methods have many drawbacks because they either fail to quickly adapt to different design... Optical multilayer thin film structures have been widely used in numerous photonic applications.However,existing inverse design methods have many drawbacks because they either fail to quickly adapt to different design targets,or are difficult to suit for different types of structures,e.g.,designing for different materials at each layer.These methods also cannot accommodate versatile design situations under different angles and polarizations.In addition,how to benefit practical fabrications and manufacturing has not been extensively considered yet.In this work,we introduce OptoGPT(Opto Generative Pretrained Transformer),a decoder-only transformer,to solve all these drawbacks and issues simultaneously. 展开更多
关键词 multilayer thin film structure inverse design foundation models deep learning structural color
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An inverse analysis of fluid flow through granular media using differentiable lattice Boltzmann method 被引量:1
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作者 Qiuyu Wang Krishna Kumar 《Journal of Rock Mechanics and Geotechnical Engineering》 SCIE CSCD 2024年第6期2077-2090,共14页
This study presents a method for the inverse analysis of fluid flow problems.The focus is put on accurately determining boundary conditions and characterizing the physical properties of granular media,such as permeabi... This study presents a method for the inverse analysis of fluid flow problems.The focus is put on accurately determining boundary conditions and characterizing the physical properties of granular media,such as permeability,and fluid components,like viscosity.The primary aim is to deduce either constant pressure head or pressure profiles,given the known velocity field at a steady-state flow through a conduit containing obstacles,including walls,spheres,and grains.The lattice Boltzmann method(LBM)combined with automatic differentiation(AD)(AD-LBM)is employed,with the help of the GPU-capable Taichi programming language.A lightweight tape is used to generate gradients for the entire LBM simulation,enabling end-to-end backpropagation.Our AD-LBM approach accurately estimates the boundary conditions for complex flow paths in porous media,leading to observed steady-state velocity fields and deriving macro-scale permeability and fluid viscosity.The method demonstrates significant advantages in terms of prediction accuracy and computational efficiency,making it a powerful tool for solving inverse fluid flow problems in various applications. 展开更多
关键词 inverse problem Fluid flow Granular media Automatic differentiation(AD) Lattice Boltzmann method(LBM)
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一类树的邻接矩阵的Moore-Penrose广义逆
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作者 王玉浩 刘奋进 徐剑锋 《吉林大学学报(理学版)》 CAS 北大核心 2024年第4期759-764,共6页
根据矩阵结构性质,利用分块矩阵技巧给出任意点数、任意长直径的毛毛虫树邻接矩阵的Moore-Penrose广义逆的具体形式,为进一步研究毛毛虫树的代数性质提供理论支撑.
关键词 邻接矩阵 分块矩阵 moore-penrose广义逆
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Application of Moore-Penrose Inverse in Deciding the Minimal Martingale Measure
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作者 Luo-gen Yao Gang Yang Xiang-qun Yang 《Acta Mathematicae Applicatae Sinica》 SCIE CSCD 2010年第4期653-660,共8页
The Moore-Penrose inverse is an important tool in algebra.This paper shows that the MoorePenrose inverse is also an effcient technique in determining the minimal martingale measure if a security price follows a semi-m... The Moore-Penrose inverse is an important tool in algebra.This paper shows that the MoorePenrose inverse is also an effcient technique in determining the minimal martingale measure if a security price follows a semi-martingale which satisfies some structure condition.We extend a result of Dzhaparidze and Spreij concerning the Moore-Penrose inverse to the case that the Moore-Penrose inverse of any matrix-valued predictable process is still predictable.Furthermore,we obtain an explicit formula of the minimal martingale measure by employing the Moore-Penrose inverse.Specifically,the minimal martingale measure in a generalized Black-Scholes model is found. 展开更多
关键词 moore-penrose inverse minimal martingale measure semi-martingales structure condition
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Fuzzy-Inverse-Model-Based Networked Tracking Control Frameworks of Time-Varying Signals
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作者 Shiwen Tong Dianwei Qian +3 位作者 Keya Yuan Dexin Liu Yuan Li Jiancheng Zhang 《IEEE/CAA Journal of Automatica Sinica》 SCIE EI CSCD 2024年第7期1708-1710,共3页
Dear Editor,Tracking control in networked environment is a very challenging problem due to the contradiction of rapid response to the time-varying signal and the inevitable delay introduced by networks. This letter ha... Dear Editor,Tracking control in networked environment is a very challenging problem due to the contradiction of rapid response to the time-varying signal and the inevitable delay introduced by networks. This letter has proposed several fuzzy-inverse-model-based network tracking control frameworks which are helpful in handling the system with nonlinear dynamics and uncertainties. 展开更多
关键词 CONTRADICTION LETTER inverse
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Triple reverse order law for the Drazin inverse
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作者 WANG Hua ZHONG Cheng-cheng 《Applied Mathematics(A Journal of Chinese Universities)》 SCIE CSCD 2024年第1期55-68,共14页
In this paper,we investigate the reverse order law for Drazin inverse of three bound-ed linear operators under some commutation relations.Moreover,the Drazin invertibility of sum is also obtained for two bounded linea... In this paper,we investigate the reverse order law for Drazin inverse of three bound-ed linear operators under some commutation relations.Moreover,the Drazin invertibility of sum is also obtained for two bounded linear operators and its expression is presented. 展开更多
关键词 Drazin inverse reverse order law space decomposition
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Uncertainty quantification of inverse analysis for geomaterials using probabilistic programming
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作者 Hongbo Zhao Shaojun Li +3 位作者 Xiaoyu Zang Xinyi Liu Lin Zhang Jiaolong Ren 《Journal of Rock Mechanics and Geotechnical Engineering》 SCIE CSCD 2024年第3期895-908,共14页
Uncertainty is an essentially challenging for safe construction and long-term stability of geotechnical engineering.The inverse analysis is commonly utilized to determine the physico-mechanical parameters.However,conv... Uncertainty is an essentially challenging for safe construction and long-term stability of geotechnical engineering.The inverse analysis is commonly utilized to determine the physico-mechanical parameters.However,conventional inverse analysis cannot deal with uncertainty in geotechnical and geological systems.In this study,a framework was developed to evaluate and quantify uncertainty in inverse analysis based on the reduced-order model(ROM)and probabilistic programming.The ROM was utilized to capture the mechanical and deformation properties of surrounding rock mass in geomechanical problems.Probabilistic programming was employed to evaluate uncertainty during construction in geotechnical engineering.A circular tunnel was then used to illustrate the proposed framework using analytical and numerical solution.The results show that the geomechanical parameters and associated uncertainty can be properly obtained and the proposed framework can capture the mechanical behaviors under uncertainty.Then,a slope case was employed to demonstrate the performance of the developed framework.The results prove that the proposed framework provides a scientific,feasible,and effective tool to characterize the properties and physical mechanism of geomaterials under uncertainty in geotechnical engineering problems. 展开更多
关键词 Geological engineering Geotechnical engineering inverse analysis Uncertainty quantification Probabilistic programming
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