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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, α-strictly diagonally dominant full matrix and α-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.

CONSTRUCTION OF FULL H-MATRICES WITH THE GIVEN EIGENVALUES BASED ON THE GIVENS MATRICES