Browsing by Author "Ferng, WR"

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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.
Mesh independence of matrix-free methods for path following
(2000-05-21)
Ferng, WR
;
Kelley, CT
;
應用數學系
;
Department of Applied Mathematics
In this paper we consider a matrix-free path following algorithm for nonlinear parameter-dependent compact fixed point problems. We show that if these problems are discretized so that certain collective compactness and strong convergence properties hold, then this algorithm can follow smooth folds and capture simple bifurcations in a mesh-independent way.
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.
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.
The shift-inverted J-Lanczos algorithm for the numerical solutions of large sparse algebraic Riccati equations
(1997-05-01)
Ferng, WR
;
Lin, WW
;
Wang, CS
;
應用數學系
;
Department of Applied Mathematics
The goal of solving an algebraic Riccati equation is to find the stable invariant subspace corresponding to all the eigenvalues lying in the open left-half plane. The purpose of this paper is to propose a structure-preserving Lanczos-type algorithm incorporated with shift and invert techniques, named shift-inverted J-Lanczos algorithm, for computing the stable invariant subspace for large sparse Hamiltonian matrices. The algorithm is based on the J-tridiagonalization procedure of a Hamiltonian matrix using symplectic similarity transformations. We give a detailed analysis on the convergence behavior of the J-Lanczos algorithm and present error bound analysis and Paige-type theorem. Numerical results for the proposed algorithm applied to a practical example arising from the position and velocity control for a string of high-speed vehicles are reported.
The shift-inverted J-Lanczos algorithm for the numerical solutions of large sparse algebraic Riccati equations (vol 33, pg 23, 1997)
(1999-08-01)
Ferng, WR
;
Lin, WW
;
Wang, CS
;
應用數學系
;
Department of Applied Mathematics