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(Anti-)Hermitian Generalized (Anti-)Hamiltonian Solution to a System of Matrix Equations

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  • Juan Yu
  • Qing-Wen Wang
  • Chang-Zhou Dong

Abstract

We mainly solve three problems. Firstly, by the decomposition of the (anti-)Hermitian generalized (anti-)Hamiltonian matrices, the necessary and sufficient conditions for the existence of and the expression for the (anti-)Hermitian generalized (anti-)Hamiltonian solutions to the system of matrix equations are derived, respectively. Secondly, the optimal approximation solution is obtained, where is the (anti-)Hermitian generalized (anti-)Hamiltonian solution set of the above system and is the given matrix. Thirdly, the least squares (anti-)Hermitian generalized (anti-)Hamiltonian solutions are considered. In addition, algorithms about computing the least squares (anti-)Hermitian generalized (anti-)Hamiltonian solution and the corresponding numerical examples are presented.

Suggested Citation

  • Juan Yu & Qing-Wen Wang & Chang-Zhou Dong, 2014. "(Anti-)Hermitian Generalized (Anti-)Hamiltonian Solution to a System of Matrix Equations," Mathematical Problems in Engineering, Hindawi, vol. 2014, pages 1-13, March.
    • Handle: RePEc:hin:jnlmpe:539215
    DOI: 10.1155/2014/539215
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