<link rel="stylesheet" href="styles.cf390c6bfbe7555f.css">

學術出版;;Publications

Permanent URI for this communityhdl:11536/1

收集所有交通大學研究人員與學生個人或團體所發表之各項學術著作，涵蓋期刊論文、教師專書、學位論文等項。;;Collections of Publications of NCTU Researchers and Students Like Journal Papers and Thesis.

Browse

🏛️國立陽明交通大學機構典藏

Author: search.filters.author.Liu, JLSubject: search.filters.subject.cubic eigenvalue problem

Search Results

Now showing 1 - 2 of 2
  • Thumbnail Image
    Item type:Item,
    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.
  • Thumbnail Image
    Item type:Item,
    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.