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Matrix form of the CGS method for solving general coupled matrix equations

Authors
Journal
Applied Mathematics Letters
0893-9659
Publisher
Elsevier
Volume
34
Identifiers
DOI: 10.1016/j.aml.2014.03.013
Keywords
  • Iterative Method
  • Cgs Method
  • Linear System
  • Kronecker Product
  • Vectorization Operator
Disciplines
  • Computer Science
  • Mathematics

Abstract

Abstract This paper deals with the problem of solving the general coupled matrix equations ∑j=1pAijXjBij=Ci,i=1,2,…,p, (including several linear matrix equations as special cases) which plays important roles in system and control theory. Based on the conjugate gradients squared (CGS) method, a simple and efficient matrix algorithm is derived to solve the general coupled matrix equations. The derived iterative algorithm is illustrated by two numerical examples and is compared with other popular iterative solvers in use today.

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