• DocumentCode
    3310816
  • Title

    The Hermitian positive definite solution of matrix equations X + A* X− A = I

  • Author

    Wei, Peiyu ; Tan, Boxue ; Liu, Xueting

  • Author_Institution
    Sch. of Electr. & Electron. Eng., Shandong Univ. of Technol., Zibo, China
  • fYear
    2009
  • fDate
    8-11 Aug. 2009
  • Firstpage
    497
  • Lastpage
    500
  • Abstract
    In this paper, we discuss the Hermitian positive definite solutions of the nonlinear matrix equation X + A* X-1 A = I. we give some necessary and sufficient conditions for the existence of a Hermitian positive definite solution of equation(1.1). Based on them, we also present some properties of the coefficient matrix A are presented and two equivalent equation of equation(1.1) when the matrix equation has a Hermitian positive definite solution. And construct an iterative methods for obtaining the Hermitian positive definite solutions of the equation are constructed.
  • Keywords
    Hermitian matrices; iterative methods; nonlinear equations; Hermitian positive definite solution; coefficient matrix; equivalent equation; iterative method; nonlinear matrix equation; Control theory; Dynamic programming; Filtering theory; Image processing; Iterative algorithms; Iterative methods; Matrix decomposition; Nonlinear equations; Stochastic processes; Sufficient conditions; Hermitian positive definite solutions; image processing; iterative method; matrix equation;
  • fLanguage
    English
  • Publisher
    ieee
  • Conference_Titel
    Computer Science and Information Technology, 2009. ICCSIT 2009. 2nd IEEE International Conference on
  • Conference_Location
    Beijing
  • Print_ISBN
    978-1-4244-4519-6
  • Electronic_ISBN
    978-1-4244-4520-2
  • Type

    conf

  • DOI
    10.1109/ICCSIT.2009.5234511
  • Filename
    5234511
    • Link To Document
    https://search.isc.ac/dl/search/defaultta.aspx?DTC=49&DC=3310816