Construction of full H-matrices with the given eigenvalues based on the Givens matrices. (English) Zbl 1455.65060
Summary: The inverse eigenvalue problem is about how to construct a desired matrix whose spectrum is the given number set. In this paper, in view of the Givens matrices, we prove that there exist three classes of full H-matrices which include strictly diagonally dominant full matrix, \( \alpha \)-strictly diagonally dominant full matrix and \(\alpha \)-double strictly diagonally dominant full matrix, and their spectrum are all the given number set. In addition, we design some numerical algorithms to explain how to construct the above-mentioned full H-matrices.
MSC:
| 65F18 | Numerical solutions to inverse eigenvalue problems |
| 15A18 | Eigenvalues, singular values, and eigenvectors |
| 15A29 | Inverse problems in linear algebra |
Keywords:
full matrix; H-matrix; strictly diagonally dominant matrix; \(\alpha\)-strictly diagonally dominant matrix; \(\alpha\)-double strictly diagonally dominant matrix; Givens matrixReferences:
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