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Recurrent neural networks for solving linear matrix equations

J. Wang
1993 Computers and Mathematics with Applications  
The proposed recurrent neural networks are shown to be asymptotically stable in the large and capable of computing inverse matrices and solving Lyapunov matrix equations.  ...  &current neural networks for solving linear matrix equations are proposed.  ...  The proposed recurrent neural networks are proven to be asymptotically stable in the large and capable of solving a variety of linear matrix equations such as inverse matrix and Lyapunov equations.  ... 
doi:10.1016/0898-1221(93)90003-e fatcat:fjrrlc23ifb2bg3dk4dfslrrqu

Global exponential stability of recurrent neural networks for synthesizing linear feedback control systems via pole assignment

Yunong Zhang, Jun Wang
2002 IEEE Transactions on Neural Networks  
The paper presents new results for recurrent neural networks applied to online computation of feedback gains of linear time-invariant multivariable systems via pole assignment.  ...  Global exponential stability is most desirable stability property of recurrent neural networks.  ...  In particular, a couple of recurrent neural networks is proposed in [9] for on-line pole assignment via solving two coupled matrix equations and the recurrent neural networks are proven to be asymptotically  ... 
doi:10.1109/tnn.2002.1000129 pmid:18244461 fatcat:sntzgqstfjh2dbdfcsloxzuayy

Global exponential stability of recurrent neural networks for solving optimization and related problems

Youshen Xia, Jun Wang
2000 IEEE Transactions on Neural Networks  
This paper studies the global exponential stability of several existing recurrent neural networks for solving linear programming problems, convex programming problems with interval constraints, convex  ...  In contrast to the existing results on global exponential stability, the present results do not require additional conditions on the weight matrices of recurrent neural networks and improve some existing  ...  INTRODUCTION Since Hopfield and Tank first proposed a recurrent neural network for solving linear programming problems [1] , many recurrent neural networks with global asymptotic stability (GAS) have  ... 
doi:10.1109/72.857782 pmid:18249829 fatcat:ix7v3dytx5bljgsqvutriuo57e

Verifying Asymptotic Time Complexity of Imperative Programs in Isabelle [article]

Bohua Zhan, Maximilian P. L. Haslbeck
2018 arXiv   pre-print
We present a framework in Isabelle for verifying asymptotic time complexity of imperative programs. We build upon an extension of Imperative HOL and its separation logic to include running time.  ...  As case studies, we verify the asymptotic time complexity (in addition to functional correctness) of imperative algorithms and data structures such as median of medians selection, Karatsuba's algorithm  ...  We thank Manuel Eberl for his impressive formalization of the Akra-Bazzi method and the functional correctness of the selection algorihtm, and Simon Wimmer for the formalization of the DP solution for  ... 
arXiv:1802.01336v1 fatcat:sencjmmrdzcdhalbbyjk2qmudm

Stability Criteria for Stochastic Recurrent Neural Networks with Two Time-Varying Delays and Impulses

R. Raja, S.Marshal Anthoni
2010 International Journal of Computer Applications  
Based on Lyapunov-Krasovskii functional and the linear matrix inequality (LMI) approach, we analyze the global asymptotic stability of impulsive neural networks.  ...  This paper is concerned with a stability problem for a class of stochastic recurrent impulsive neural networks with both discrete and distributed time-varying delays.  ...  ACKNOWLEDGEMENTS The work of the first author was supported by UGC Rajiv Gandhi National Fellowship and the work of the second author was supported by the CSIR, New Delhi.  ... 
doi:10.5120/514-831 fatcat:26wa6tvj4rglrpjx6yrwweahha

Resurrecting the asymptotics of linear recurrences

Jet Wimp, Doron Zeilberger
1985 Journal of Mathematical Analysis and Applications  
Once on the forefront of mathematical research in America, the asymptotics of the solutions of linear recurrence equations is now almost forgotten, especially by the people who need it most, namely combinatorists  ...  Here we present this theory in a concise form and give a number of examples that should enable the practicing combinatorist and computer scientist to include this important technique in her (or his) asymptotics  ...  COMBINATORIAL FAMILIES COUNTED BY SOLVING A LINEAR RECURRENCE EQUATION EXAMPLE 1.1.  ... 
doi:10.1016/0022-247x(85)90209-4 fatcat:wayakacw6fc2paalzly6e2l7nq

On the number of proper k-colorings in an n-gon [article]

Shantanu Chhabra
2013 arXiv   pre-print
Often, for huge values of $n$ and $k$, it becomes impractical to display the output numbers, which would consist of thousands of digits. We report the answer modulo a certain number.  ...  The proposed algorithm can easily be solved to obtain the explicit expression.  ...  This linear recurrence relation can be solved to obtain the explicit formula, which confirms the correctness of the proposed linear recurrence relation.  ... 
arXiv:1312.4398v1 fatcat:bliilhqlwvfe7kxefsxynea5j4

Global exponential stability of neural networks with globally Lipschitz continuous activations and its application to linear variational inequality problem

Xue-Bin Liang, J. Si
2001 IEEE Transactions on Neural Networks  
As a demonstration, we apply the obtained analysis results to the design of a recurrent neural network (RNN) for solving the linear variational inequality problem (VIP) defined on any nonempty and closed  ...  the widely used sigmoidal activations and the piecewise linear activations.  ...  ACKNOWLEDGMENT The authors would like to thank the Associate Editor and the anonymous reviewers for their helpful comments and suggestions.  ... 
doi:10.1109/72.914529 pmid:18244389 fatcat:gsbsyjftwvcajkyvppawlsv6dm

Universal Average-Case Optimality of Polyak Momentum [article]

Damien Scieur, Fabian Pedregosa
2021 arXiv   pre-print
This brings a new perspective on this classical method, showing that PM is asymptotically both worst-case and average-case optimal.  ...  In this work we establish a novel link between PM and the average-case analysis.  ...  and relevant remarks.  ... 
arXiv:2002.04664v4 fatcat:3hm7uex4qng4lfyvx4x63xevl4

A new algorithm for solving Toeplitz systems of equations

Frank de Hoog
1987 Linear Algebra and its Applications  
The recurrences used are closely related to the Zohar-Trench and Bareiss algorithms but do not have any obvious connection with other asymptotically fast algorithms for the inversion of Toeplitz systems  ...  We present some recurrences that are the basis for an algorithm to invert an n x n Toeplitz system of linear equations with computational complexity 0( n log2 n).  ...  INTRODUCTION The problem of finding the solution of the system of linear equations T,,y = h, 0.1) where y,h E C" and T, E C" X C" is a Toeplitz matrix, arises in many data processing applications, such  ... 
doi:10.1016/0024-3795(87)90107-8 fatcat:hxpiry6mbbdjfhbn2y76t262y4

Heights in Generalized Tries and PATRICIA Tries [chapter]

Charles Knessl, Wojciech Szpankowski
2000 Lecture Notes in Computer Science  
We derive these results by a combination of analytic methods such as generating functions, Mellin transform, the saddle point method and ideas of applied mathematics such as linearization, asymptotic matching  ...  iS is concentrated at k I , however, there exist subsequences of n such that the mass is on the two points hI -1 and hI, or k I and hi + 1.  ...  solve the linear recurrence (4.48) for b(k), subject to b(l) = 1.  ... 
doi:10.1007/10719839_31 fatcat:fm5cpkhysnbqjm2jztvwcgbsei

Solving Pseudomonotone Variational Inequalities and Pseudoconvex Optimization Problems Using the Projection Neural Network

Xiaolin Hu, Jun Wang
2006 IEEE Transactions on Neural Networks  
In recent years, a recurrent neural network called projection neural network was proposed for solving monotone variational inequalities and related convex optimization problems.  ...  Under various pseudomonotonicity conditions and other conditions, the projection neural network is proved to be stable in the sense of Lyapunov and globally convergent, globally asymptotically stable,  ...  In view of the equivalent formulation of VI in (2), the following recurrent neural network, called projection neural network for solving (1) is developed in [24] - [28] (4) where and are two scaling  ... 
doi:10.1109/tnn.2006.879774 pmid:17131663 fatcat:acgv5m7rkbfrljdvxa6carmwsu

Cubic spline solutions of boundary value problems over infinite intervals

Mohan K. Kadalbajoo, K.Santhana Raman
1986 Journal of Computational and Applied Mathematics  
The stability of the method is analysed and the theory is illustrated by solving test examples.  ...  The tridiagonal system resulting from the spline approximation is efficiently solved by the method of sweeps.  ...  To cite a few, Bickley [5] has considered the use of cubic splines for solving linear two-point boundary value problems, which leads to the solution of a set of linear equations whose coefficient matrix  ... 
doi:10.1016/0377-0427(86)90219-0 fatcat:bmlhapklsfayhaoznfan6wknle

An Algorithm for Solving Second Order Nonlinear Singular Perturbation Boundary Value Problems

E. R. El-Zahar, Y. S. Hassanein
2011 Journal of Modern Methods in Numerical Mathematics  
The algorithm is derived based on the piecewise linearization of the obtained IVP and its analytical integration over a non-uniform mesh.  ...  The step size is determined directly according to the variation of the solution within a step in the boundary layer region and results in two-term recurrence relation with controlled step size.  ...  Reddy and Chakravarthy [14] presented a method of reduction of order for solving linear and a class of nonlinear SPBVPs.  ... 
doi:10.20454/jmmnm.2011.71 fatcat:ut2yzly3dfaubm5r4as344wo4y

A Lagrangian network for kinematic control of redundant robot manipulators

Jun Wang, Qingni Hu, Danchi Jiang
1999 IEEE Transactions on Neural Networks  
Index Terms-Asymptotic stability, kinematic control, kinematically redundant manipulators, optimization method, recurrent neural networks.  ...  The proposed Lagrangian network is shown to be capable of asymptotic tracking for the motion control of kinematically redundant manipulators.  ...  It is shown to be asymptotically stable and capable of solving the inverse kinematics problem in real time.  ... 
doi:10.1109/72.788651 pmid:18252613 fatcat:3wqblkwcpzbuxgjsjgapdrroqq
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