New SOR-like methods for solving the Sylvester equation

Jakub Kierzkowski

Open Mathematics (2015)

  • Volume: 13, Issue: 1, page 178-187, electronic only
  • ISSN: 2391-5455

Abstract

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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.

How to cite

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Jakub Kierzkowski. "New SOR-like methods for solving the Sylvester equation." Open Mathematics 13.1 (2015): 178-187, electronic only. <http://eudml.org/doc/268698>.

@article{JakubKierzkowski2015,
abstract = {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.},
author = {Jakub Kierzkowski},
journal = {Open Mathematics},
keywords = {Sylvester equation; SOR-like iterative method; Iterative methods; iterative methods; successive overrelaxation; numerical experimentation},
language = {eng},
number = {1},
pages = {178-187, electronic only},
title = {New SOR-like methods for solving the Sylvester equation},
url = {http://eudml.org/doc/268698},
volume = {13},
year = {2015},
}

TY - JOUR
AU - Jakub Kierzkowski
TI - New SOR-like methods for solving the Sylvester equation
JO - Open Mathematics
PY - 2015
VL - 13
IS - 1
SP - 178
EP - 187, electronic only
AB - 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.
LA - eng
KW - Sylvester equation; SOR-like iterative method; Iterative methods; iterative methods; successive overrelaxation; numerical experimentation
UR - http://eudml.org/doc/268698
ER -

References

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  1. [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. [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. [3] Datta, B., Numerical Methods for Linear Control Systems, Elsevier Science, 2004 
  4. [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] Zbl0421.65022
  5. [5] Hu D.Y., Reichel L., Krylov-subspace methods for the Sylvester equation, Linear Algebra Appl., 1992, 172, 283-313 Zbl0777.65028
  6. [6] Lancaster, P., Tismenetsky, M., The theory of matrices: with applications, 2nd ed., Academic Press, Orlando, 1985 Zbl0558.15001
  7. [7] Roth W.E., The equations AX - YB = C and AX - XB = C in matrices, Proc. Amer. Math. Soc., 1952, 3(3), 392-396 Zbl0047.01901
  8. [8] Simoncini, V., On the numerical solution of AX - XB = C, BIT, 1996, 36(4), 814-830 [Crossref] Zbl0863.65022
  9. [9] Starke G., Niethammer W., SOR for AX - XB = C, Linear Algebra Appl., 1991, 154/156, 355-375 
  10. [10] Woźnicki, Z.I., Solving linear systems: an analysis of matrix prefactorization iterative methods, Matrix Editions, 2009 Zbl1170.65002

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