• DocumentCode
    823924
  • Title

    Direct solution method for A_{1} E + EA_{2} = -D

  • Author

    Bickart, Theodore A.

  • Author_Institution
    Syracuse University, Syracuse, NY, USA
  • Volume
    22
  • Issue
    3
  • fYear
    1977
  • fDate
    6/1/1977 12:00:00 AM
  • Firstpage
    467
  • Lastpage
    468
  • Abstract
    A direct method-a method without truncation or convergence errors-for the solution of A_{1} E + EA_{2} = - D , where A_{1} \\in R^{n_{1} \\times n_{1}} and A_{2} \\in R^{n_{2} \\times n_{2}} , is described. The only assumption on the matrices A1and A2is that the spectra of A1and -A_{2} be disjoint. The method requires storage for order 2n_{1}^{2}+3n_{1}n_{2}+2n_{2}^{2} variables and requires order n{1}(n_{1}^{2}+ n_{1}n_{2} + n_{2}^{2})n_{2} multiplications and divisions.
  • Keywords
    Matrix equations; Approximation algorithms; Computer errors; Eigenvalues and eigenfunctions; Equations; Finite wordlength effects; Iterative methods; Matrices; Polynomials;
  • fLanguage
    English
  • Journal_Title
    Automatic Control, IEEE Transactions on
  • Publisher
    ieee
  • ISSN
    0018-9286
  • Type

    jour

  • DOI
    10.1109/TAC.1977.1101490
  • Filename
    1101490
    • Link To Document
    https://search.isc.ac/dl/search/defaultta.aspx?DTC=49&DC=823924