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Iterative solutions to the extended Sylvester-conjugate matrix equations. (English) Zbl 1223.65032
The authors investigate the extended Sylvester-conjugate matrix equation AXB+CX ¯D=F, where A,C m×r , B,D s×n and F m×n are known matrices, and X r×s is the matrix to be determined. They present an iterative algorithm to solve the extended Sylvester-conjugate matrix equation and a sufficient condition to guarantee that the proposed algorithm converges to the exact solution for arbitrary initial matrix. In addition, a more general Sylvester-conjugate matrix equation of the form i=1 p A i XB i + j=1 q C j X ¯D j =F is also considered in this paper, where A i ,C j m×r , B i ,D j s×n (1ip,1jq) and F m×n are known matrices, and X r×s is the matrix to be determined, and the convergence analysis is given as well.
MSC:
65F30Other matrix algorithms
15A24Matrix equations and identities
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