The numerical solution of $X = A_{1}X + XA_{2} + D, X(0) = C$

Author

Davison, E.J.

Author_Institution

University of Toronto, Toronto, Ontario, Canada

Volume

Issue

fYear

1975

fDate

8/1/1975 12:00:00 AM

Firstpage

566

Lastpage

567

Abstract

The numerical solution of the general matrix differential equation $\\dot{X} = A_{1}X + XA_{2} + D, X(0) = C$ for $X$ is considered where A1and A2are stable matrices. The algorithm proposed requires only $8n^{2}$ words of memory (for large $n$ ) and converges in approximately $50n^{3} \\mu$ s where μ is the multiplication time of the digital computer, and $n = \\max (n_{1},n_{2})$ where $A_{1} \\in R^{n_{1} \\times n_{1}} , A_{2} \\in R^{n_{2} \\times n_{2}}$ . The algorithm is particularly suitable for systems where $n$ is large (e.g, $n \\gg 10$ ).

Keywords

Differential equations; Matrix equations; Numerical integration; Councils; Degradation; Differential equations; Drilling; Eigenvalues and eigenfunctions; Iterative algorithms; Matrices; Notice of Violation; Random variables; Upper bound;

fLanguage

English

Journal_Title

Automatic Control, IEEE Transactions on

Publisher

ieee

ISSN

0018-9286

Type

jour

DOI

10.1109/TAC.1975.1101033

Filename

1101033

Link To Document

https://search.isc.ac/dl/search/defaultta.aspx?DTC=49&DC=819472