Browsing by Author "Lin, WW"

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A novel nonsymmetric K_-Lanczos algorithm for the generalized nonsymmetric K_-eigenvalue problems
(1997-02-01)
Ferng, WR
;
Lin, KY
;
Lin, WW
;
應用數學系
;
Department of Applied Mathematics
In this article, we present a novel algorithm, named nonsymmetric K---Lanczos algorithm, for computing a few extreme eigenvalues of the generalized eigenvalue problem Mx = lambda Lx, where the matrices M and L have the so-called K-+/--structures. We demonstrate a K---tridiagonalization procedure preserves the K-+/--structures. An error bound for the extreme K---Ritz value obtained from this new algorithm is presented. When compared with the class nonsymmetric Lanczos approach, this method has the same order of computational complexity and can be viewed as a special 2 x 2-block nonsymmetric Lanczos algorithm. Numerical experiments with randomly generated K---matrices show that our algorithm converges faster and more accurate than the nonsymmetric Lanczos algorithm. (C) Elsevier Science Inc., 1997
A novel nonsymmetric K_-Lanczos algorithm for the generalized nonsymmetric K_-eigenvalue problems
(1997-02-01)
Ferng, WR
;
Lin, KY
;
Lin, WW
;
應用數學系
;
Department of Applied Mathematics
In this article, we present a novel algorithm, named nonsymmetric K---Lanczos algorithm, for computing a few extreme eigenvalues of the generalized eigenvalue problem Mx = lambda Lx, where the matrices M and L have the so-called K-+/--structures. We demonstrate a K---tridiagonalization procedure preserves the K-+/--structures. An error bound for the extreme K---Ritz value obtained from this new algorithm is presented. When compared with the class nonsymmetric Lanczos approach, this method has the same order of computational complexity and can be viewed as a special 2 x 2-block nonsymmetric Lanczos algorithm. Numerical experiments with randomly generated K---matrices show that our algorithm converges faster and more accurate than the nonsymmetric Lanczos algorithm. (C) Elsevier Science Inc., 1997
A structure-preserving Lanczos-type algorithm with application to control problems
(1997)
Ferng, WR
;
Lin, WW
;
Wang, CS
;
應用數學系
;
Department of Applied Mathematics
A Hamiltonian structure-preserving Lanczos-type method, named the J-Lanczos algorithm, is introduced for solving large sparse Hamiltonian eigenvalue problem which arises in both continuous-time and discrete-time optimal control applications. Shift and invert techniques are incorporated to approximate all stable eigenvalues and the associated invariant subspace. Numerical results for solving high order continuous-time Riccati equation arising from position and velocity control for a string of high speed vechicles are presented.
A synchronization scheme using self-pulsating laser diodes in optical chaotic communication
(2000-03-01)
Juang, C
;
Hwang, TM
;
Juang, J
;
Lin, WW
;
應用數學系
A synchronization scheme using self-pulsating laser diodes in optical chaotic communication is proposed. Optical chaotic light can be obtained by injecting a sinusoidal electronic signal into a self-pulsating laser diode. To synchronize between two identical chaotic systems with different initial conditions, a drive and response system model is constructed according to Pecora and Carroll's theory. Synchronization can be achieved for optical simplex and duplex transmissions provided that the conditional Lyapunov exponents for the drive and response systems are all negative. This approach offers a key step toward realizing optical chaotic modulation and demodulation.
Bifurcations and chaos in two-cell cellular neural networks with periodic inputs
(2004-09-01)
Lin, SS
;
Lin, WW
;
Yang, TH
;
應用數學系
;
Department of Applied Mathematics
This study investigates bifurcations and chaos in two-cell Cellular Neural Networks (CNN) with periodic inputs. Without the inputs, the time periodic solutions are obtained for template A = [r, p, s] with p > 1, r > p - 1 and -s > p - 1. The number of periodic solutions can be proven to be no more than two in exterior regions. The input is b sin 2pit/T with period T > 0 and amplitude b > 0. The typical trajectories Gamma(b, T, A) and their omega-limit set omega(b, T, A) vary with b, T and A are also considered. The asymptotic limit cycles A,,(T, A) with period T of Gamma(b, T, A) are obtained as b --> infinity. When T-0 less than or equal to T-0* (given in (67)), Lambda(infinity) and -Lambda(infinity) can be separated. The onset of chaos can be induced by crises of omega(b, T, A) and -omega(b, T, A) for suitable T and b. The ratio A(b) = aT(b)/a(1)(b), of largest amplitude a(1)(b) except for T-mode and amplitude of the T-mode of the Fast Fourier Transform (FFT) of r(b, T, A), can be used to compare the strength of sustained periodic cycle Lambdao(A) and the inputs. When A(b) much less than 1, Lambda(o)(A) dominates and the attractor omega(b, T, A) is either a quasi-periodic or a periodic. Moreover, the range b of the window of periodic cycles constitutes a devil's staircase. When A(b) similar to 1, finitely many chaotic regions and window regions exist and interweave with each other. In each window, the basic periodic cycle can be identified. A sequence of period-doubling is observed to the left of the basic periodic cycle and a quasi-periodic region is observed to the right of it. For large b, the input dominates, omega(b, T, A) becomes simpler, from quasi-periodic to periodic as b increases.
Cellular neural networks: Local patterns for general templates
(2000-07-01)
Hsu, CH
;
Juang, J
;
Lin, SS
;
Lin, WW
;
應用數學系
This work investigates the mosaic local patterns for cellular neural networks with general templates. Our results demonstrate that the set of templates can be divided into many finite regions. In each region, the same family of local patterns can be generated. Conversely, our results further demonstrate that some templates can realize a family of local patterns which can be linearly separated by a hyperplane in the configuration space. This study also proposes algorithms for verifying the linear separability for a given family of local patterns and, when it is separable, for obtaining the associated template.
Chaotic behaviors of bistable laser diodes and its application in synchronization of optical communication
(2001-10-01)
Wang, WC
;
Hwang, TM
;
Juang, C
;
Juang, J
;
Liu, CY
Period-doubling routes to chaos behavior in bistable laser diodes is examined numerically, An external sinusoidal electronic drive is injected to generate chaotic light output. Phase portrait, Poincare map, bifurcation diagram, and Lyapunov exponent are then calculated to assert the existence of chaos. Furthermore, according to Pecora and Carroll's theory, a drive-response system is constructed by using the bistable laser diodes to mask the sinusoidal electronic signal with chaotic light. Synchronization can be achieved for optical simplex and duplex transmissions using bistable laser diodes. The proposed synchronization scheme between two separate chaotic systems provides a key step toward optical chaotic communication.
Eigenvalue problems for one-dimensional discrete Schrodinger operators with symmetric boundary conditions
(2001-11-19)
Juang, J
;
Lin, WW
;
Shieh, SF
;
應用數學系
;
Department of Applied Mathematics
In this paper, we investigate the one-dimensional discrete Schrodinger equation with general, symmetric boundary conditions. Our results primarily concern the number of energy states lying in the wells.
Fixed-point methods for a semiconductor quantum dot model
(2004-09-01)
Hwang, TM
;
Lin, WW
;
Liu, JL
;
Wang, WC
;
應用數學系
This paper presents various fixed-point methods for computing the ground state energy and its associated wave function of a semiconductor quantum dot model. The discretization of the three-dimensional Schrodinger equation leads to a large-scale cubic matrix polynomial eigenvalue problem for which the desired eigenvalue is embedded in the interior of the spectrum. The cubic problem is reformulated in several forms so that the desired eigenpair becomes a fixed point of the new formulations. Several algorithms are then proposed for solving the fixed-point problem. Numerical results show that the simple fixed-point method with acceleration schemes can be very efficient and stable. (C) 2004 Elsevier Ltd. All rights reserved.
FM detection from an optical chaotic carrier
(2001-07-01)
Huang, ST
;
Hwang, TM
;
Juang, C
;
Juang, J
;
Lin, WW
To synchronize two identical chaotic systems with different initial conditions, a drive and response system model is constructed according to Pecora and Carroll's theory. The drive and response systems become asymptotically synchronized if an FM signal is added to the drive system. The FM signal can be detected when the drive and response systems are strongly coupled.
Jacobi-Davidson methods for cubic eigenvalue problems
(2005-09-01)
Hwang, TM
;
Lin, WW
;
Liu, JL
;
Wang, WC
;
應用數學系
Several Jacobi-Davidson type methods are proposed for computing interior eigenpairs of large-scale cubic eigenvalue problems. To successively compute the eigenpairs, a novel explicit non-equivalence deflation method with low-rank updates is developed and analysed. Various techniques such as locking, search direction transformation, restarting, and preconditioning are incorporated into the methods to improve stability and efficiency. A semiconductor quantum dot model is given as an example to illustrate the cubic nature of the eigenvalue system resulting from the finite difference approximation. Numerical results of this model are given to demonstrate the convergence and effectiveness of the methods. Comparison results are also provided to indicate advantages and disadvantages among the various methods. Copyright (c) 2004 John Wiley & Sons, Ltd.
Nonequivalence transformation of lambda-matrix eigenproblems and model embedding approach to model tuning
(2001-01-01)
Ferng, WR
;
Lin, WW
;
Pierce, DJ
;
Wang, CS
;
應用數學系
In this paper we present some theory for a non-equivalence transformation of matrix eigenvalues for lambda -matrix polynomials. Application of this transformation to eigenvalue embedding for model tuning on a realistic industry problem is illustrated. The new approach has several advantages such as flexibility, efficiency, and structure-preservation. A numerical experiment on a pseudosimulation data set from The Boeing Company is retorted. Copyright (C) 2001 John Wiley & Sons, Ltd.
Nonsymmetric algebraic Riccati equations and Hamiltonian-like matrices
(1998-09-22)
Juang, J
;
Lin, WW
;
應用數學系
;
Department of Applied Mathematics
We consider a nonsymmetric algebraic matrix Riccati equation arising from transport theory. The nonnegative solutions of the equation can be explicitly constructed via the inversion formula of a Cauchy matrix. An error analysis and numerical results are given. We also show a comparison theorem of the nonnegative solutions.
Nonsymmetric algebraic Riccati equations and Hamiltonian-like matrices
(1998-09-22)
Juang, J
;
Lin, WW
;
應用數學系
;
Department of Applied Mathematics
We consider a nonsymmetric algebraic matrix Riccati equation arising from transport theory. The nonnegative solutions of the equation can be explicitly constructed via the inversion formula of a Cauchy matrix. An error analysis and numerical results are given. We also show a comparison theorem of the nonnegative solutions.
Numerical algorithms for undamped gyroscopic systems
(1999-01-01)
Ferng, WR
;
Lin, WW
;
Wang, CS
;
應用數學系
;
Department of Applied Mathematics
The solutions of a gyroscopic vibrating system oscillating about an equilibrium position, with no external applied forces and no damping forces, are completely determined by the quadratic eigenvalue problem (-lambda(i)(2)M + lambda(i)G + K)x(i) = 0, for i = 1, ..., 2n, where M, G, and K are real n x n matrices, and M is symmetric positive definite (denoted by M > 0), G is skew symmetric, and either K > 0 or -K > 0. Gyroscopic systemin motion about a stable equilibrium position (with -K > 0) are well understood. Two Lanczos-type algorithms, the pseudo skew symmetric Lanczos algorithm and the J-Lanczos algorithm, are studied for computing some extreme eigenpairs for solving gyroscopic systems in motion about an unstable equilibrium position (with K > 0). Shift and invert strategies, error bounds, implementation issues, and numerical results for both algorithms are presented in details. (C) 1998 Elsevier Science Ltd. All rights reserved.
Numerical methods for semiconductor heterostructures with band nonparabolicity
(2003-09-01)
Wang, WC
;
Hwang, TM
;
Lin, WW
;
Liu, JL
;
應用數學系
This article presents numerical methods for computing bound state energies and associated wave functions of three-dimensional semiconductor heterostructures with special interest in the numerical treatment of the effect of band nonparabolicity. A nonuniform finite difference method is presented to approximate a model of a cylindrical-shaped semiconductor quantum dot embedded in another semiconductor matrix. A matrix reduction method is then proposed to dramatically reduce huge eigenvalue systems to relatively very small subsystems. Moreover, the nonparabolic band structure results in a cubic type of nonlinear eigenvalue problems for which a cubic Jacobi-Davidson method with an explicit nonequivalence deflation method are proposed to compute all the desired eigenpairs. Numerical results are given to illustrate the spectrum of energy levels and the corresponding wave functions in rather detail. (C) 2003 Elsevier B.V. All rights reserved.
On computing stable Lagrangian subspaces of Hamiltonian matrices and symplectic pencils
(1997-07-01)
Lin, WW
;
Wang, CS
;
應用數學系
;
Department of Applied Mathematics
This paper presents algorithms far computing stable Lagrangian invariant subspaces of a Hamiltonian matrix and a symplectic pencil, respectively, having purely imaginary and unimodular eigenvalues. The problems often arise in solving continuous- or discrete-time H-infinity-optimal control, linear-quadratic control and filtering theory, etc. The main approach of our algorithms is to determine an isotropic Jordan subbasis corresponding to purely imaginary (unimodular) eigenvalues by using the associated Jordan basis of the square of the Hamiltonian matrix (the S + S-1-transformation of. the symplectic pencil). The algorithms preserve structures and are numerically efficient and reliable in that they employ only orthogonal transformations in the continuous case.
On computing stable Lagrangian subspaces of Hamiltonian matrices and symplectic pencils
(1997-07-01)
Lin, WW
;
Wang, CS
;
應用數學系
;
Department of Applied Mathematics
This paper presents algorithms far computing stable Lagrangian invariant subspaces of a Hamiltonian matrix and a symplectic pencil, respectively, having purely imaginary and unimodular eigenvalues. The problems often arise in solving continuous- or discrete-time H-infinity-optimal control, linear-quadratic control and filtering theory, etc. The main approach of our algorithms is to determine an isotropic Jordan subbasis corresponding to purely imaginary (unimodular) eigenvalues by using the associated Jordan basis of the square of the Hamiltonian matrix (the S + S-1-transformation of. the symplectic pencil). The algorithms preserve structures and are numerically efficient and reliable in that they employ only orthogonal transformations in the continuous case.
Optical chaotic AM demodulation by asymptotic synchronization
(2000-02-01)
Juang, C
;
Hwang, TM
;
Juang, J
;
Lin, WW
;
應用數學系
Synchronization between two identical chaotic systems (drive and response) with different initial conditions can be achieved provided that the conditional Lyapunov exponents are all negative. Adding an AM signal to the drive system, the two systems become asymptotically synchronized. The AM signal can be recovered by utilizing the property of the asymptotic synchronization. Chaotic AM noise is present as a direct result of the chaotic AM demodulation. Signal-to-chaotic-AM-noise ratio is calculated as a function of the signal amplitude.
Optoelectronic delayed-feedback and chaos in quantum-well laser diodes
(2001-05-15)
Juang, C
;
Huang, CC
;
Hwang, TM
;
Juang, J
;
Lin, WW
Electronic-controlled route to chaos in a quantum-well laser diode is carried out by a delayed-feedback technique. By introducing an extra delayed-feedback control term cS(n)(t - tau), chaotic light output can be achieved at relatively low bias and small modulation depth. Bifurcation diagram, Poincare map, and Lyapunov exponents suggests quasi-periodicity route to chaos. (C) 2001 Elsevier Science B.V. All rights reserved.