Amit Bhaya - Academia.edu (original) (raw)
Papers by Amit Bhaya
International Journal of Hybrid Intelligent Systems, 2014
ABSTRACT This paper revisits a class of recently proposed so-called invariant manifold methods fo... more ABSTRACT This paper revisits a class of recently proposed so-called invariant manifold methods for zero finding of ill-posed problems, showing that they can be profitably viewed as homotopy methods, in which the homotopy parameter is interpreted as a learning parameter. Moreover, it is shown that the choice of this learning parameter can be made in a natural manner from a control Liapunov function approach CLF. From this viewpoint, maintaining manifold invariance is equivalent to ensuring that the CLF satisfies a certain ordinary differential equation, involving the learning parameter, that allows an estimate of rate of convergence. In order to illustrate this approach, algorithms recently proposed using the invariant manifold approach, are rederived, via CLFs, in a unified manner. Adaptive regularization parameters for solving linear algebraic ill-posed problems were also proposed. This paper also shows that the discretizations of the ODEs to solve the zero finding problem, as well as the different adaptive choices of the regularization parameter, yield iterative methods for linear systems, which are also derived using the Liapunov optimizing control LOC method.
AIP Conference Proceedings, 2009
Numerical methods are implemented in digital computers using finite precision arithmetics, in whi... more Numerical methods are implemented in digital computers using finite precision arithmetics, in which real∕ complex numbers are represented by finite length words. This representation results in truncating∕ rounding off the numbers, which leads to numerical errors in the algorithms. The numerical errors can result in the loss of some properties of the numerical methods (for example, the orthogonality of the residues of the conjugate gradient), which, in turn, cause numerical instability. In this paper, a new model of the perturbations resulting ...
Siam Review, Jun 1, 1998
Page 1. REAL MATRICES WITH POSITIVE DETERMINANT ARE HOMOTOPIC TO THE IDENTITY ∗ AMIT BHAYA† SIAM ... more Page 1. REAL MATRICES WITH POSITIVE DETERMINANT ARE HOMOTOPIC TO THE IDENTITY ∗ AMIT BHAYA† SIAM REV. c 1998 Society for Industrial and Applied Mathematics Vol. 40, No. 2, pp. 335–340, June 1998 012 Abstract. The statement that is the title of this note is given a novel proof using the ideas of controllability and eigenvalue assignment from linear system theory. Key words. homotopy, degree theory, determinants, matrices, controllability, eigenvalue assignment AMS subject classifications. 15A15, 55M25, 93B05, 93B55 PII. ...
Ijsysc, 1995
The condition number k (S) of a matrix S is the ratio of the largest singular value of S to the s... more The condition number k (S) of a matrix S is the ratio of the largest singular value of S to the smallest, and is a very important quantity in the sensitivity and convergence analysis of many problems in numerical linear algebra. The optimal condition number of a matrix S is the minimum, over all positive diagonal matrices P, of K;(PS). In this paper we interpret the problem of finding the optimal preconditioner P that minimizes k (PS) as the equivalent problem of maximally clustering the poles of a suitably defined dynamical system by the ...
Http Dx Doi Org 10 1080 0020718508961165, May 21, 2007
ABSTRACT
Proceedings of Iscas 95 International Symposium on Circuits and Systems, Dec 20, 1995
This book gives a presentation of new methods related to dynamical systems described by linear an... more This book gives a presentation of new methods related to dynamical systems described by linear and nonlinear ordinary differential equations and difference equations. Special attention is paid to dynamical systems that are open to analysis by the Liapunov approach. The material will interest researchers and professionals in control engineering or those working in scientific computation or the stability of dynamical systems.
2009 International Joint Conference on Neural Networks, Jun 14, 2009
Abstract This paper presents a unified approach to the design of neural networks that aim to mini... more Abstract This paper presents a unified approach to the design of neural networks that aim to minimize scalar nonconvex functions that have continuous first-and second-order derivatives and a unique global minimum. The approach is based on interpreting the function as a controlled object, namely one that has an output (the function value) that has to be driven to its smallest value by suitable manipulation of its inputs: this is achieved by the use of the control Liapunov function (CLF) technique, well known in systems and control ...
Neurocomputing, Oct 1, 2009
Signal Processing, Oct 1, 2010
Multi-user mobile communication systems use adaptive and linearly constrained adaptive filters fo... more Multi-user mobile communication systems use adaptive and linearly constrained adaptive filters for blind and non-blind adaptive interference cancelation, multipath reduction, equalization, and adaptive beamforming. A conjugate gradient and a steepest descent method for real-time processing are proposed and applied to blind adaptive array processor. Simulations show that the proposed algorithms have performance comparable to those of algorithms proposed earlier.
49Th Ieee Conference on Decision and Control, 2010
Abstract This paper introduces a new paradigm, called cooperative computation, for the solution o... more Abstract This paper introduces a new paradigm, called cooperative computation, for the solution of systems of linear equations with symmetric coefficient matrices. The simplest version of the algorithm consists of two agents, each one computing the solution of the whole system, using an iterative method. Infrequent unidirectional communication occurs from one agent to the other, either periodically, or probabilistically, thus characterizing the computation as parallel and asynchronous. Every time one agent communicates its ...
International Journal of Signal Processing, Image Processing and Pattern Recognition, 2014
2008 IEEE International Joint Conference on Neural Networks (IEEE World Congress on Computational Intelligence), 2008
Proceedings of the 2002 International Joint Conference on Neural Networks. IJCNN'02 (Cat. No.02CH37290), 2000
International Journal of Hybrid Intelligent Systems, 2014
ABSTRACT This paper revisits a class of recently proposed so-called invariant manifold methods fo... more ABSTRACT This paper revisits a class of recently proposed so-called invariant manifold methods for zero finding of ill-posed problems, showing that they can be profitably viewed as homotopy methods, in which the homotopy parameter is interpreted as a learning parameter. Moreover, it is shown that the choice of this learning parameter can be made in a natural manner from a control Liapunov function approach CLF. From this viewpoint, maintaining manifold invariance is equivalent to ensuring that the CLF satisfies a certain ordinary differential equation, involving the learning parameter, that allows an estimate of rate of convergence. In order to illustrate this approach, algorithms recently proposed using the invariant manifold approach, are rederived, via CLFs, in a unified manner. Adaptive regularization parameters for solving linear algebraic ill-posed problems were also proposed. This paper also shows that the discretizations of the ODEs to solve the zero finding problem, as well as the different adaptive choices of the regularization parameter, yield iterative methods for linear systems, which are also derived using the Liapunov optimizing control LOC method.
AIP Conference Proceedings, 2009
Numerical methods are implemented in digital computers using finite precision arithmetics, in whi... more Numerical methods are implemented in digital computers using finite precision arithmetics, in which real∕ complex numbers are represented by finite length words. This representation results in truncating∕ rounding off the numbers, which leads to numerical errors in the algorithms. The numerical errors can result in the loss of some properties of the numerical methods (for example, the orthogonality of the residues of the conjugate gradient), which, in turn, cause numerical instability. In this paper, a new model of the perturbations resulting ...
Siam Review, Jun 1, 1998
Page 1. REAL MATRICES WITH POSITIVE DETERMINANT ARE HOMOTOPIC TO THE IDENTITY ∗ AMIT BHAYA† SIAM ... more Page 1. REAL MATRICES WITH POSITIVE DETERMINANT ARE HOMOTOPIC TO THE IDENTITY ∗ AMIT BHAYA† SIAM REV. c 1998 Society for Industrial and Applied Mathematics Vol. 40, No. 2, pp. 335–340, June 1998 012 Abstract. The statement that is the title of this note is given a novel proof using the ideas of controllability and eigenvalue assignment from linear system theory. Key words. homotopy, degree theory, determinants, matrices, controllability, eigenvalue assignment AMS subject classifications. 15A15, 55M25, 93B05, 93B55 PII. ...
Ijsysc, 1995
The condition number k (S) of a matrix S is the ratio of the largest singular value of S to the s... more The condition number k (S) of a matrix S is the ratio of the largest singular value of S to the smallest, and is a very important quantity in the sensitivity and convergence analysis of many problems in numerical linear algebra. The optimal condition number of a matrix S is the minimum, over all positive diagonal matrices P, of K;(PS). In this paper we interpret the problem of finding the optimal preconditioner P that minimizes k (PS) as the equivalent problem of maximally clustering the poles of a suitably defined dynamical system by the ...
Http Dx Doi Org 10 1080 0020718508961165, May 21, 2007
ABSTRACT
Proceedings of Iscas 95 International Symposium on Circuits and Systems, Dec 20, 1995
This book gives a presentation of new methods related to dynamical systems described by linear an... more This book gives a presentation of new methods related to dynamical systems described by linear and nonlinear ordinary differential equations and difference equations. Special attention is paid to dynamical systems that are open to analysis by the Liapunov approach. The material will interest researchers and professionals in control engineering or those working in scientific computation or the stability of dynamical systems.
2009 International Joint Conference on Neural Networks, Jun 14, 2009
Abstract This paper presents a unified approach to the design of neural networks that aim to mini... more Abstract This paper presents a unified approach to the design of neural networks that aim to minimize scalar nonconvex functions that have continuous first-and second-order derivatives and a unique global minimum. The approach is based on interpreting the function as a controlled object, namely one that has an output (the function value) that has to be driven to its smallest value by suitable manipulation of its inputs: this is achieved by the use of the control Liapunov function (CLF) technique, well known in systems and control ...
Neurocomputing, Oct 1, 2009
Signal Processing, Oct 1, 2010
Multi-user mobile communication systems use adaptive and linearly constrained adaptive filters fo... more Multi-user mobile communication systems use adaptive and linearly constrained adaptive filters for blind and non-blind adaptive interference cancelation, multipath reduction, equalization, and adaptive beamforming. A conjugate gradient and a steepest descent method for real-time processing are proposed and applied to blind adaptive array processor. Simulations show that the proposed algorithms have performance comparable to those of algorithms proposed earlier.
49Th Ieee Conference on Decision and Control, 2010
Abstract This paper introduces a new paradigm, called cooperative computation, for the solution o... more Abstract This paper introduces a new paradigm, called cooperative computation, for the solution of systems of linear equations with symmetric coefficient matrices. The simplest version of the algorithm consists of two agents, each one computing the solution of the whole system, using an iterative method. Infrequent unidirectional communication occurs from one agent to the other, either periodically, or probabilistically, thus characterizing the computation as parallel and asynchronous. Every time one agent communicates its ...
International Journal of Signal Processing, Image Processing and Pattern Recognition, 2014
2008 IEEE International Joint Conference on Neural Networks (IEEE World Congress on Computational Intelligence), 2008
Proceedings of the 2002 International Joint Conference on Neural Networks. IJCNN'02 (Cat. No.02CH37290), 2000