Least-squares solutions of generalized inverse eigenvalue problem over Hermitian–Hamiltonian matrices with a submatrix constraint
- Huzhou University, School of Science (China)
- Southeast University, Department of Mathematics (China)
In this paper, a gradient-based iterative algorithm is proposed for finding the least-squares solutions of the following constrained generalized inverse eigenvalue problem: given X∈C{sup n×m}, Λ=diag(λ{sub 1},λ{sub 2},…,λ{sub m})∈C{sup m×m}, find A{sup ∗},B{sup ∗}∈C{sup n×n}, such that ∥AX−BXΛ∥ is minimized, where A{sup ∗},B{sup ∗} are Hermitian–Hamiltonian except for a special submatrix. For any initial constrained matrices, a solution pair (A{sup ∗},B{sup ∗}) can be obtained in finite iteration steps by this iterative algorithm in the absence of roundoff errors. The least-norm solution can be obtained by choosing a special kind of initial matrix pencil. In addition, the unique optimal approximation solution to a given matrix pencil in the solution set of the above problem can also be obtained. A numerical example is given to show the efficiency of the proposed algorithm.
- OSTI ID:
- 22783973
- Journal Information:
- Computational and Applied Mathematics, Journal Name: Computational and Applied Mathematics Journal Issue: 1 Vol. 37; ISSN 0101-8205
- Country of Publication:
- United States
- Language:
- English
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