New SOR-like methods for solving the Sylvester equation
Jakub Kierzkowski
Open Mathematics, Tome 13 (2015), / Harvested from The Polish Digital Mathematics Library

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.

Publié le : 2015-01-01
EUDML-ID : urn:eudml:doc:268698
@article{bwmeta1.element.doi-10_1515_math-2015-0017,
     author = {Jakub Kierzkowski},
     title = {New SOR-like methods for solving the Sylvester equation},
     journal = {Open Mathematics},
     volume = {13},
     year = {2015},
     zbl = {1309.65049},
     language = {en},
     url = {http://dml.mathdoc.fr/item/bwmeta1.element.doi-10_1515_math-2015-0017}
}
Jakub Kierzkowski. New SOR-like methods for solving the Sylvester equation. Open Mathematics, Tome 13 (2015) . http://gdmltest.u-ga.fr/item/bwmeta1.element.doi-10_1515_math-2015-0017/

[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] | Zbl 0421.65022

[5] Hu D.Y., Reichel L., Krylov-subspace methods for the Sylvester equation, Linear Algebra Appl., 1992, 172, 283-313 | Zbl 0777.65028

[6] Lancaster, P., Tismenetsky, M., The theory of matrices: with applications, 2nd ed., Academic Press, Orlando, 1985 | Zbl 0558.15001

[7] Roth W.E., The equations AX - YB = C and AX - XB = C in matrices, Proc. Amer. Math. Soc., 1952, 3(3), 392-396 | Zbl 0047.01901

[8] Simoncini, V., On the numerical solution of AX - XB = C, BIT, 1996, 36(4), 814-830 [Crossref] | Zbl 0863.65022

[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 | Zbl 1170.65002