Construction of full H-matrices with the given eigenvalues based on the Givens matrices

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.