Iterative methods for enclosing the solution set of the parametric Sylvester matrix equation

Document Type : Original Paper

Author

Department of Mathematics, Shahid Chamran University of Ahvaz, Ahvaz, Iran

Abstract

In this paper, we study the parametric Sylvester matrix equation A(p)X+XB(p)=C(p) whose elements are linear functions of some parameters varying within intervals. We first present some characterizations of its solution set and then using these characterizations, we give some sufficient conditions for boundedness of the solution set. We then propose two efficient iterative methods to find some enclosures to the solution set. The introduced iterative methods reduce the computational costs of enclosing the solution set of our problem with respect to the other methods, considerably. Finally, by some numerical methods we show the effectiveness of the proposed methods.

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References

[1] Frommer, A. and Hashemi, B. (2012). Verified error bounds for solutions of Sylvester matrix equations, Linear Algebra and its Applications, 436, 405-420.
[2] Hajarian, M. (2016). Generalized conjugate direction algorithm for solving the general coupled matrix equations over symmetric matrices, Numerical Algorithms, 73, 591–609.
[3] Hajarian, M. (2017). New finite algorithm for solving the generalized nonhomogeneous Yakubovich‐Transpose matrix equation, Numerical Algorithms, 19, 164-172.
[4] Jansson, C. (1991). Interval linear systems with symmetric matrices, skewsymmetric matrices and dependencies in the right hand side, Computing, 46, 265-274.
[5] Rump, S.M. (1994). Verification methods for dense and sparse systems of equations, in Elsevier, Amsterdam.
Journal of Advanced Mathematical Modeling
Volume 8, Issue 1
September 2018
Pages 95-117

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History

  • Receive Date: 09 November 2017
  • Revise Date: 19 August 2018
  • Accept Date: 16 August 2018

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