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Recurrent Neural Networks for Computing the moore-penrose inverse with Momentum Learning

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Chinese Journal of Electronics 2020年第6期29卷 1039-1045页

作者： ZHANG Naimin ZHANG Ting Department of Mathematics Wenzhou University

We are concerned with a kind of iterative method for computing the moore-penrose inverse,which can be considered as a discrete-time form of recurrent neural networks.We study the momentum learning scheme of the method and discuss its semi-convergence when computing the moore-penrose inverse of a rankdeficient matrix.We prove the semi-convergence for our new acceleration algorithm and obtain the optimal momentum factor which makes the fastest semi-convergence.Numerical tests demonstrate the effectiveness of our new acceleration algorithm.

关键词： Recurrent neural networks Momentum learning moore-penrose inverse Semi-convergence

Application of moore-penrose inverse in Deciding the Minimal Martingale Measure

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Acta Mathematicae Applicatae Sinica 2010年第4期26卷 653-660页

作者： Luo-gen Yao Gang Yang Xiang-qun Yang Information Department of Hunan Business College Changsha 410205China College of Mathematics and Computer Science Hunan Normal UniversityChangsha 410081China

The moore-penrose inverse is an important tool in algebra. This paper shows that the moore-penrose inverse is also an efficient 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.

关键词： moore-penrose inverse minimal martingale measure semi-martingales structure condition

The Reverse Order Law for moore-penrose inverse of Closed Operators

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Chinese Quarterly Journal of Mathematics 2013年第1期28卷 139-146页

作者： DU Fa-peng XUE Yi-feng School of Mathematical and Physical Sciences Xuzhou Institute of Technology Xuzhou 221008 China Department of Mathematics East China Normal University Shanghai 200241 China

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... 详细信息

关键词： reverse order law norm-preserving extension moore-penrose inverse

Unified Approach to the Expression for the moore-penrose inverse of a- xy

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Chinese Quarterly Journal of Mathematics 2014年第3期29卷 465-474页

作者： D U Fa-peng XUE Yi-feng Department of Mathematics School of mathematical and Physical Sciences Xuzhou Institute of Technology Xuzhou 221008 China Department of Mathematics East China Normal University Shanghai 200241 China

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

Some Equalities and Inequalities for the Hermitian moore-penrose inverse of Triple Matrix Product with Applications

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Journal of Mathematical Research with Applications 2015年第3期35卷 321-329页

作者： Yongge TIAN Wenxing GUO China Economics and Management Academy Central University of Finance and Economics School of Statistics and Mathematics Central University of Finance and Economics

We investigate relationships between the moore-penrose inverse(ABA*)and the product [(AB)(1,2,3)]*B(AB)(1,2,3)through some rank and inertia formulas for the difference of(ABA*)-[(AB)(1,2,3)]*B(AB)(1,2,3),where B is Hermitian matrix and(AB)(1,2,3)is a {1,2,3}-inverse of AB.We show that there always exists an(AB)(1,2,3)such that(ABA*)= [(AB)(1,2,3)]*B(AB)(1,2,3)holds.In addition,we also establish necessary and sufficient conditions for the two inequalities(ABA*) [(AB)(1,2,3)]*B(AB)(1,2,3)and(ABA*)[(AB)(1,2,3)]*B(AB)(1,2,3)to hold in the L¨owner partial ordering.Some variations of the equalities and inequalities are also presented.In particular,some equalities and inequalities for the moore-penrose inverse of the sum A + B of two Hermitian matrices A and B are established.

关键词： moore-penrose inverse reverse-order law rank inertia Lwner partial ordering

星图相关矩阵的moore-penrose广义逆

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New Identities for moore-penrose inverses of Some Operator Products and Their Reverse-order Laws

运筹与模糊学 2024年第2期14卷 191-199页

作者：王玉浩长安大学理学院，陕西西安

本文利用矩阵的低秩性、分块性等性质给出了星图的邻接矩阵、关联矩阵、距离矩阵、拉普拉斯矩阵和无符号拉普拉斯矩阵的moore-penrose广义逆。以上结论对进一步研究星图的代数性质提供了理论支撑，同时对研究其他图类的相关矩阵的广义... 详细信息

本文利用矩阵的低秩性、分块性等性质给出了星图的邻接矩阵、关联矩阵、距离矩阵、拉普拉斯矩阵和无符号拉普拉斯矩阵的moore-penrose广义逆。以上结论对进一步研究星图的代数性质提供了理论支撑，同时对研究其他图类的相关矩阵的广义逆提供了理论参考。

关键词：星图分块矩阵 moore-penrose广义逆 Star Graph Block Matrix moore-penrose inverse

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Acta Mathematica Sinica,English Series 2023年第12期39卷 2414-2426页

作者： Mehdi MOHAMMADZADEH KARIZAKI Javad FAROKHI-OSTAD Department of Computer Engineering University of Torbat HeydariehTorbat Heydarieh***Iran Department of Basic Sciences Birjand University of TechnologyBirjand***Iran

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... 详细信息

关键词： moore-penrose inverse Reverse-order Law

Splitting of Operators and Operator Equations

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Acta Mathematica Sinica,English Series 2023年第6期39卷 1085-1100页

作者： Chun Yuan DENG Wan Yu ZHANG School of Mathematics Science South China Normal UniversityGuangzhou 510631P.R.China

In this paper,we consider the splitting operators into the product of two positive operators.For given operators A and T∈B(H)with A≥0 and R(A)=R(T),if T can be splitted as T=AX for some positive operator X,then the existence of X and the properties of T are studied.The related research are the solutions of operator equations T=XAX and TX=XAX,which have some particular properties and broad applications in many fields.The conditions for the existence of solutions or idempotent solutions of these kinds of equations are studied and new representations of the general solutions are given.

关键词： Projection positive operator operator equation moore-penrose inverse

Linear-quadratic optimal control for time-varying descriptor systems via space decompositions

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The Journal of China Universities of Posts and Telecommunications 2023年第6期30卷 38-48页

作者： LüPengchao Huang Junjie Liu Bo School of Mathematical Sciences Inner Mongolia UniversityHohhot 010021China Ministry of Education Key Laboratory for Intelligent Analysis and Security Governance of Ethnic Languages Minzu University of ChinaBeijing 100081China

This paper aims at solving the linear-quadratic optimal control problems(LQOCP)for time-varying descriptor systems in a real Hilbert space.By using the moore-penrose inverse theory and space decomposition technique,the descriptor system can be rewritten as a new differential-algebraic equation(DAE),and then some novel sufficient conditions for the solvability of LQOCP are obtained.Especially,the methods proposed in this work are simpler and easier to verify and compute,and can solve LQOCP without the range inclusion condition.In addition,some numerical examples are shown to verify the results obtained.

关键词： linear-quadratic optimal control problem(LQOCP) time-varying descriptor system moore-penrose inverse space decomposition