Let H∈Cn×n be an n×n unitary upper Hessenberg matrix whose subdiagonal elements are all positive. Partition H as H=[H11 H12 H21 H22],(0.1) where H11 is its k×k leading principal submatrix; H22 is the c...Let H∈Cn×n be an n×n unitary upper Hessenberg matrix whose subdiagonal elements are all positive. Partition H as H=[H11 H12 H21 H22],(0.1) where H11 is its k×k leading principal submatrix; H22 is the complementary matrix of H11. In this paper, H is constructed uniquely when its eigenvalues and the eigenvalues of (H|^)11 and (H|^)22 are known. Here (H|^)11 and (H|^)22 are rank-one modifications of H11 and H22 respectively.展开更多
基金This work is supported by the Natural Science Foundation of Fujian Province of China （No. Z0511010）the Natural Science Foundation of China （No. 10571012）.
文摘Let H∈Cn×n be an n×n unitary upper Hessenberg matrix whose subdiagonal elements are all positive. Partition H as H=[H11 H12 H21 H22],(0.1) where H11 is its k×k leading principal submatrix; H22 is the complementary matrix of H11. In this paper, H is constructed uniquely when its eigenvalues and the eigenvalues of (H|^)11 and (H|^)22 are known. Here (H|^)11 and (H|^)22 are rank-one modifications of H11 and H22 respectively.
