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Recurrent neural networks for solving linear matrix equations

1993
*
Computers and Mathematics with Applications
*

The proposed

doi:10.1016/0898-1221(93)90003-e
fatcat:fjrrlc23ifb2bg3dk4dfslrrqu
*recurrent*neural networks are shown to be*asymptotically*stable in the large*and*capable*of*computing inverse matrices*and**solving*Lyapunov matrix equations. ... ¤t 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. ...##
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Global exponential stability of recurrent neural networks for synthesizing linear feedback control systems via pole assignment

2002
*
IEEE Transactions on Neural Networks
*

The paper presents new results for

doi:10.1109/tnn.2002.1000129
pmid:18244461
fatcat:sntzgqstfjh2dbdfcsloxzuayy
*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*...##
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Global exponential stability of recurrent neural networks for solving optimization and related problems

2000
*
IEEE Transactions on Neural Networks
*

This paper studies the global exponential stability

doi:10.1109/72.857782
pmid:18249829
fatcat:ix7v3dytx5bljgsqvutriuo57e
*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 ...##
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Verifying Asymptotic Time Complexity of Imperative Programs in Isabelle
[article]

2018
*
arXiv
*
pre-print

We present a framework in Isabelle for

arXiv:1802.01336v1
fatcat:sencjmmrdzcdhalbbyjk2qmudm
*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 ...##
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Stability Criteria for Stochastic Recurrent Neural Networks with Two Time-Varying Delays and Impulses

2010
*
International Journal of Computer Applications
*

Based on Lyapunov-Krasovskii functional

doi:10.5120/514-831
fatcat:26wa6tvj4rglrpjx6yrwweahha
*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. ...##
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Resurrecting the asymptotics of linear recurrences

1985
*
Journal of Mathematical Analysis and Applications
*

Once on the forefront

doi:10.1016/0022-247x(85)90209-4
fatcat:wayakacw6fc2paalzly6e2l7nq
*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. ...##
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On the number of proper k-colorings in an n-gon
[article]

2013
*
arXiv
*
pre-print

Often, for huge values

arXiv:1312.4398v1
fatcat:bliilhqlwvfe7kxefsxynea5j4
*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. ...##
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Global exponential stability of neural networks with globally Lipschitz continuous activations and its application to linear variational inequality problem

2001
*
IEEE Transactions on Neural Networks
*

As a demonstration, we apply the obtained analysis results to the design

doi:10.1109/72.914529
pmid:18244389
fatcat:gsbsyjftwvcajkyvppawlsv6dm
*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. ...##
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Universal Average-Case Optimality of Polyak Momentum
[article]

2021
*
arXiv
*
pre-print

This brings a new perspective on this classical method, showing that PM is

arXiv:2002.04664v4
fatcat:3hm7uex4qng4lfyvx4x63xevl4
*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. ...##
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A new algorithm for solving Toeplitz systems of equations

1987
*
Linear Algebra and its Applications
*

The

doi:10.1016/0024-3795(87)90107-8
fatcat:hxpiry6mbbdjfhbn2y76t262y4
*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 ...##
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Heights in Generalized Tries and PATRICIA Tries
[chapter]

2000
*
Lecture Notes in Computer Science
*

We derive these results by a combination

doi:10.1007/10719839_31
fatcat:fm5cpkhysnbqjm2jztvwcgbsei
*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. ...##
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Solving Pseudomonotone Variational Inequalities and Pseudoconvex Optimization Problems Using the Projection Neural Network

2006
*
IEEE Transactions on Neural Networks
*

In recent years, a

doi:10.1109/tnn.2006.879774
pmid:17131663
fatcat:acgv5m7rkbfrljdvxa6carmwsu
*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 ...##
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Cubic spline solutions of boundary value problems over infinite intervals

1986
*
Journal of Computational and Applied Mathematics
*

The stability

doi:10.1016/0377-0427(86)90219-0
fatcat:bmlhapklsfayhaoznfan6wknle
*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 ...##
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An Algorithm for Solving Second Order Nonlinear Singular Perturbation Boundary Value Problems

2011
*
Journal of Modern Methods in Numerical Mathematics
*

The algorithm is derived based on the piecewise

doi:10.20454/jmmnm.2011.71
fatcat:ut2yzly3dfaubm5r4as344wo4y
*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. ...##
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A Lagrangian network for kinematic control of redundant robot manipulators

1999
*
IEEE Transactions on Neural Networks
*

Index Terms-

doi:10.1109/72.788651
pmid:18252613
fatcat:3wqblkwcpzbuxgjsjgapdrroqq
*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. ...
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