• DocumentCode
    3159986
  • Title

    On the extreme solutions of an nonlinear matrix equation

  • Author

    Guo, Xiaoxia ; Ji, Zhijian

  • Author_Institution
    Ocean Univ. of China, Qingdao
  • fYear
    2007
  • fDate
    9-13 July 2007
  • Firstpage
    1642
  • Lastpage
    1647
  • Abstract
    A quadratically convergent algorithm (QCA) for solving the extreme solutions of the matrix equation AX2+BX+C=0 was proposed by Bini and Meini. In this paper, we present a new derivation for this algorithm and a new proof for the convergence theory by using a structure-preserving transformation of a matrix pencil. Since only the knowledge of the elementary matrix theory is used, the derivation and the proof are very concise and pellucid.
  • Keywords
    matrix algebra; nonlinear equations; convergence theory; elementary matrix theory; matrix pencil; nonlinear matrix equation; quadratically convergent algorithm; structure-preserving transformation; Cities and towns; Control theory; Convergence; Design for quality; Eigenvalues and eigenfunctions; Newton method; Nonlinear equations; Quantum cellular automata; Riccati equations; Solvents;
  • fLanguage
    English
  • Publisher
    ieee
  • Conference_Titel
    American Control Conference, 2007. ACC '07
  • Conference_Location
    New York, NY
  • ISSN
    0743-1619
  • Print_ISBN
    1-4244-0988-8
  • Electronic_ISBN
    0743-1619
  • Type

    conf

  • DOI
    10.1109/ACC.2007.4282233
  • Filename
    4282233
    • Link To Document
    https://search.isc.ac/dl/search/defaultta.aspx?DTC=49&DC=3159986