zbMATH — the first resource for mathematics

Examples
Geometry Search for the term Geometry in any field. Queries are case-independent.
Funct* Wildcard queries are specified by * (e.g. functions, functorial, etc.). Otherwise the search is exact.
"Topological group" Phrases (multi-words) should be set in "straight quotation marks".
au: Bourbaki & ti: Algebra Search for author and title. The and-operator & is default and can be omitted.
Chebyshev | Tschebyscheff The or-operator | allows to search for Chebyshev or Tschebyscheff.
"Quasi* map*" py: 1989 The resulting documents have publication year 1989.
so: Eur* J* Mat* Soc* cc: 14 Search for publications in a particular source with a Mathematics Subject Classification code (cc) in 14.
"Partial diff* eq*" ! elliptic The not-operator ! eliminates all results containing the word elliptic.
dt: b & au: Hilbert The document type is set to books; alternatively: j for journal articles, a for book articles.
py: 2000-2015 cc: (94A | 11T) Number ranges are accepted. Terms can be grouped within (parentheses).
la: chinese Find documents in a given language. ISO 639-1 language codes can also be used.

Operators
a & b logic and
a | b logic or
!ab logic not
abc* right wildcard
"ab c" phrase
(ab c) parentheses
Fields
any anywhere an internal document identifier
au author, editor ai internal author identifier
ti title la language
so source ab review, abstract
py publication year rv reviewer
cc MSC code ut uncontrolled term
dt document type (j: journal article; b: book; a: book article)
On matrix equations $X - AXF = C$ and $X - A\overline{X}F = C$. (English) Zbl 05580666

MSC:
15A24Matrix equations and identities
WorldCat.org
Full Text: DOI
References:
[1] Bartels, R. H.; Stewart, G. W.: A solution of the equation AX+XB=C, Commun. ACM 15, 820-826 (1972)
[2] Kitagawa, G.: An algorithm for solving the matrix equation X=FXFT+S., Int. J. Control 25, 745-753 (1977) · Zbl 0364.65025 · doi:10.1080/00207177708922266
[3] Kleinman, D. L.; Rao, P. K.: Extensions to the bartels--stewart algorithm for linear matrix equation, IEEE trans. Automat. control 23, No. 1, 85-87 (1978) · Zbl 0369.65005 · doi:10.1109/TAC.1978.1101681
[4] Golub, G.; Nash, S.; Van Loan, C.: A Hessenberg--Schur method for the problem AX+XB=C, IEEE trans. Automat. control 24, 909-913 (1979) · Zbl 0421.65022 · doi:10.1109/TAC.1979.1102170
[5] Betser, A.; Cohen, N.; Zeheb, E.: On solving the Lyapunov and Stein equations for a companion matrix, System control lett. 25, 211-218 (1995) · Zbl 0877.93043 · doi:10.1016/0167-6911(94)00072-4
[6] Ma, E. C.: A finite series solution of the matrix equation AX-XB=C, SIAM J. Appl. math. 14, 490-495 (1966) · Zbl 0144.27003 · doi:10.1137/0114043
[7] Brockett, R. W.: Introduction to matrix analysis, (1970)
[8] Young, N. J.: Formulae for the solution of Lyapunov matrix equation, Internat. J. Control 31, 159-179 (1980) · Zbl 0432.93050 · doi:10.1080/00207178008961035
[9] Desouza, E.; Bhattacharyya, S.: Controllability and observability and the solution of AX-XB=C, Linear algebra appl. 39, 167-188 (1981) · Zbl 0468.15012 · doi:10.1016/0024-3795(81)90301-3
[10] Zhou, B.; Duan, G. R.: An explicit solution to the matrix equation AX-XF=BY, Linear algebra appl. 402, 345-366 (2005) · Zbl 1076.15016 · doi:10.1016/j.laa.2005.01.018
[11] Jones, J.; Charleslew, J. R.: Solutions of the Lyapunov matrix equation BX-XA=C., IEEE trans. Automat. control 27, No. 2, 464-466 (1982)
[12] Hanzon, B.: A Faddeev sequence method for solving Lyapunov and Sylvester equations, Linear algebra appl., 401-430 (1996) · Zbl 0859.65038 · doi:10.1016/0024-3795(95)00683-4
[13] Jameson, A.: Solution of the equation AX-XB=C by inversion of an $M{\times}$M or $N{\times}$N matrix, SIAM J. Appl. math. 16, 1020-1023 (1968) · Zbl 0169.35202 · doi:10.1137/0116083
[14] Jiang, T.; Wei, M.: On solutions of the matrix equations X-AXB=C and X-ax\bar{}b=C, Linear algebra appl. 367, 225-233 (2003) · Zbl 1019.15002 · doi:10.1016/S0024-3795(02)00633-X
[15] Wu, A. G.; Duan, G. R.: Solution to the generalized Sylvester matrix equation AV+BW=EVF, IET control theory appl. 1, No. 1, 402-408 (2007)
[16] Wu, A. G.; Fu, Y. M.; Duan, G. R.: On solutions of the matrix equations V-AVF=BW and V-av\bar{}f=BW, Math. comput. Modelling 47, 1181-1197 (2008) · Zbl 1145.15302 · doi:10.1016/j.mcm.2007.06.024
[17] Lewis, F. L.: Further remarks on the Cayley--Hamilton theorem and leverrier’s method for matrix pencil (sE-A), IEEE trans. Automat. control 31, No. 9, 869-870 (1986) · Zbl 0601.15010 · doi:10.1109/TAC.1986.1104420