Least-squares solutions of generalized inverse eigenvalue problem over Hermitian–Hamiltonian matrices with a submatrix constraint

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 n × m , Λ = diag ( λ 1 , λ 2 , … , λ m ) ∈ C m × m , find A ∗ , B ∗ ∈ C n × n , such that ‖ A X - B X Λ ‖ is minimi...

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Veröffentlicht in:Computational & applied mathematics Jg. 37; H. 1; S. 593 - 603
Hauptverfasser: Cai, Jing, Chen, Jianlong
Format: Journal Article
Sprache:Englisch
Veröffentlicht: Cham Springer International Publishing 01.03.2018
Springer Nature B.V
Schlagworte:
Algorithms
Applications of Mathematics
Applied physics
Computational mathematics
Computational Mathematics and Numerical Analysis
Eigenvalues
Generalized inverse
Iterative algorithms
Iterative methods
Least squares
Mathematical Applications in Computer Science
Mathematical Applications in the Physical Sciences
Mathematics
Mathematics and Statistics
Matrix
Roundoff error
Hermitian–Hamiltonian matrix
65J22
Optimal approximation
Submatrix constraint
Generalized inverse eigenvalue problem
15A29
ISSN:0101-8205, 2238-3603, 1807-0302
Online-Zugang:Volltext
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Zusammenfassung: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 n × m , Λ = diag ( λ 1 , λ 2 , … , λ m ) ∈ C m × m , find A ∗ , B ∗ ∈ C n × n , such that ‖ A X - B X Λ ‖ is minimized, where A ∗ , B ∗ are Hermitian–Hamiltonian except for a special submatrix. For any initial constrained matrices, a solution pair ( A ∗ , B ∗ ) 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.
Bibliographie:ObjectType-Article-1
SourceType-Scholarly Journals-1
ObjectType-Feature-2
content type line 14
ISSN:0101-8205
2238-3603
1807-0302
DOI:10.1007/s40314-016-0363-3