Warianty tytułu
Języki publikacji
Abstrakty
We present new iterative methods for solving the Sylvester equation belonging to the class of SOR-like methods, based on the SOR (Successive Over-Relaxation) method for solving linear systems. We discuss convergence characteristics of the methods. Numerical experimentation results are included, illustrating the theoretical results and some other noteworthy properties of the Methods.
Słowa kluczowe
Wydawca
Czasopismo
Rocznik
Tom
Numer
Opis fizyczny
Daty
otrzymano
2013-12-07
zaakceptowano
2014-12-06
online
2014-12-23
Twórcy
autor
-
Faculty of Mathematics and Computer Science, Warsaw University of Technology,
Koszykowa 75, 00-662, Warsaw, Poland, J.Kierzkowski@mini.pw.edu.pl
Bibliografia
- [1] Bartels, R.H., Stewart G.W., Algorithm 432: the solution of the matrix equation AX - BX D C, Communications of the ACM,1972, 15(9), 820-826
- [2] Beineke, L.W., Wilson, R.J. (Eds.), Topics in Algebraic Graph Theory, Encyclopedia Math. Appl., Cambridge University Press,102, Cambridge University Press, 2005
- [3] Datta, B., Numerical Methods for Linear Control Systems, Elsevier Science, 2004
- [4] Golub G.H., Nash S., Van Loan C., Hessenberg–Schur method for the problem AX + C XB = C, IEEE Trans. Automat. Control,1979, AC-24(6), 909-913[Crossref]
- [5] Hu D.Y., Reichel L., Krylov-subspace methods for the Sylvester equation, Linear Algebra Appl., 1992, 172, 283-313
- [6] Lancaster, P., Tismenetsky, M., The theory of matrices: with applications, 2nd ed., Academic Press, Orlando, 1985
- [7] Roth W.E., The equations AX - YB = C and AX - XB = C in matrices, Proc. Amer. Math. Soc., 1952, 3(3), 392-396
- [8] Simoncini, V., On the numerical solution of AX - XB = C, BIT, 1996, 36(4), 814-830[Crossref]
- [9] Starke G., Niethammer W., SOR for AX - XB = C, Linear Algebra Appl., 1991, 154/156, 355-375
- [10] Woźnicki, Z.I., Solving linear systems: an analysis of matrix prefactorization iterative methods, Matrix Editions, 2009
Typ dokumentu
Bibliografia
Identyfikatory
Identyfikator YADDA
bwmeta1.element.doi-10_1515_math-2015-0017