In this paper, four inverse eigenproblems with given three eigenvalues and cor-responding eigenvectors are considered, some necessary and sufficient conditionsunder which there exists a unique solution for these probl...In this paper, four inverse eigenproblems with given three eigenvalues and cor-responding eigenvectors are considered, some necessary and sufficient conditionsunder which there exists a unique solution for these problems are given. Further-more some numerical algorithms and some numerical experiments are given.展开更多
This paper considers the problem of constructing a Jacobi matrix from its defec tive eigen-pair and a principal submatrix. Some necessary and sufficient conditions of solvability have been derived. An algorithm and tw...This paper considers the problem of constructing a Jacobi matrix from its defec tive eigen-pair and a principal submatrix. Some necessary and sufficient conditions of solvability have been derived. An algorithm and two numerical examples have been given.展开更多
Let T1,n be an n x n unreduced symmetric tridiagonal matrix with eigenvaluesand is an (n - 1) x (n - 1) submatrix by deleting the kth row and kth column, k = 1, 2,be the eigenvalues of T1,k andbe the eigenvalues of Tk...Let T1,n be an n x n unreduced symmetric tridiagonal matrix with eigenvaluesand is an (n - 1) x (n - 1) submatrix by deleting the kth row and kth column, k = 1, 2,be the eigenvalues of T1,k andbe the eigenvalues of Tk+1,nA new inverse eigenvalues problem has put forward as follows: How do we construct anunreduced symmetric tridiagonal matrix T1,n, if we only know the spectral data: theeigenvalues of T1,n, the eigenvalues of Ti,k-1 and the eigenvalues of Tk+1,n?Namely if we only know the data: A1, A2, An,how do we find the matrix T1,n? A necessary and sufficient condition and an algorithm ofsolving such problem, are given in this paper.展开更多
文摘In this paper, four inverse eigenproblems with given three eigenvalues and cor-responding eigenvectors are considered, some necessary and sufficient conditionsunder which there exists a unique solution for these problems are given. Further-more some numerical algorithms and some numerical experiments are given.
文摘This paper considers the problem of constructing a Jacobi matrix from its defec tive eigen-pair and a principal submatrix. Some necessary and sufficient conditions of solvability have been derived. An algorithm and two numerical examples have been given.
基金Project 19771020 supported by National Science Foundation of China.
文摘Let T1,n be an n x n unreduced symmetric tridiagonal matrix with eigenvaluesand is an (n - 1) x (n - 1) submatrix by deleting the kth row and kth column, k = 1, 2,be the eigenvalues of T1,k andbe the eigenvalues of Tk+1,nA new inverse eigenvalues problem has put forward as follows: How do we construct anunreduced symmetric tridiagonal matrix T1,n, if we only know the spectral data: theeigenvalues of T1,n, the eigenvalues of Ti,k-1 and the eigenvalues of Tk+1,n?Namely if we only know the data: A1, A2, An,how do we find the matrix T1,n? A necessary and sufficient condition and an algorithm ofsolving such problem, are given in this paper.
