Iterative orthogonal direction methods for Hermitian minimum norm solutions of two consistent matrix equations

@article{Deng2006IterativeOD,
  title={Iterative orthogonal direction methods for Hermitian minimum norm solutions of two consistent matrix equations},
  author={Yuanzheng Deng and Zhong-Zhi Bai and Yong-Hua Gao},
  journal={Numerical Lin. Alg. with Applic.},
  year={2006},
  volume={13},
  pages={801-823}
}
The consistent conditions and the general expressions about the Hermitian solutions of the linear matrix equations AXB =C and (AX, XB)= (C, D) are studied in depth, where A, B, C and D are given matrices of suitable sizes. The Hermitian minimum F-norm solutions are obtained for the matrix equations AXB = C and (AX, XB)= (C, D) by Moore–Penrose generalized inverse, respectively. For both matrix equations, we design iterative methods according to the fundamental idea of the classical conjugate… CONTINUE READING
24 Citations
35 References
Similar Papers

Citations

Publications citing this paper.
Showing 1-10 of 24 extracted citations

References

Publications referenced by this paper.
Showing 1-10 of 35 references

Hermitian and nonnegative definite solutions of linear matrix equations

  • C Khatri, S. Mitra
  • SIAM Journal on Applied Mathematics
  • 1976
Highly Influential
4 Excerpts

A generalised inverse for matrices

  • R. Penrose
  • Mathematical Proceedings of the Cambridge…
  • 1955
Highly Influential
16 Excerpts

The optimal solution of linear matrix equations by using matrix decompositions

  • Yuan Y-X
  • Mathematica Numerica Sinica
  • 2002
Highly Influential
3 Excerpts

A hybrid preconditioner of banded matrix approximation and alternating direction implicit iteration for symmetric sinc-Galerkin linear systems

  • M Ng, Bai Z-Z
  • Linear Algebra and its Applications
  • 2003

Iterative Krylov Methods for Large Linear Systems

  • H. Van der Vorst
  • 2003

Similar Papers

Loading similar papers…