• DocumentCode
    834069
  • Title

    A time-stepping procedure for Ẋ=A1X+XA2+D, X(0)=C

  • Author

    Serbin, Steven M. ; Serbin, Cynthia A.

  • Author_Institution
    University of Tennessee, Knoxville, TN, USA
  • Volume
    25
  • Issue
    6
  • fYear
    1980
  • fDate
    12/1/1980 12:00:00 AM
  • Firstpage
    1138
  • Lastpage
    1141
  • Abstract
    We develop an expression for the exact solution of the matrix differential problem \\dot{X} = A_{1} X + XA_{2} + D, X(0) = C based on variation of parameters and use this to devise the time-stepping relation X(t+h)=e^{A_{1}h}{X(t)+\\int\\liminf {0}\\limsup {h}e^{-A_{1}s}De^{-A_{2}s}ds}e^{A_{2}h} . We modify a procedure of Van Loan to effect efficient computation of all the terms necessary to advance the solution in time according to this relation. We consider some alternatives when sparsity is a concern. A numerical example of our procedure is included.
  • Keywords
    Equations; Iterative algorithms; Mathematics; Sparse matrices; Statistics;
  • fLanguage
    English
  • Journal_Title
    Automatic Control, IEEE Transactions on
  • Publisher
    ieee
  • ISSN
    0018-9286
  • Type

    jour

  • DOI
    10.1109/TAC.1980.1102495
  • Filename
    1102495
    • Link To Document
    https://search.isc.ac/dl/search/defaultta.aspx?DTC=49&DC=834069