论文信息 - Some inverse eigenproblems for Jacobi and arrow matrices

Some inverse eigenproblems for Jacobi and arrow matrices

We consider the problem of reconstructing Jacobi matrices and real symmetric arrow matrices from two eigenpairs. Algorithms for solving these inverse problems are presented. We show that there are reasonable conditions under which this reconstruction is always possible. Moreover, it is seen that in certain cases reconstruction can proceed with little or no cancellation. The algorithm is particularly elegant for the tridiagonal matrix associated with a bidiagonal singular value decomposition.

[1] Carlos F. Borges,et al. On Model Identification of Gaussian Reciprocal Processes from the Eigenstructure of their Covariances , 1993 .

[2] B. Parlett. The Symmetric Eigenvalue Problem , 1981 .

[3] Carlos F. Borges,et al. A Parallel Divide and Conquer Algorithm for the Generalized Real Symmetric Definite Tridiagonal Eigenproblem , 1993 .

[4] Gene H. Golub,et al. A modified method for reconstructing periodic Jacobi matrices , 1984 .

[5] Eigenvector matrices of symmetric tridiagonals , 1984 .

[6] J. H. Wilkinson. The algebraic eigenvalue problem , 1966 .

[7] W. Gragg,et al. On computing accurate singular values and eigenvalues of matrices with acyclic graphs , 1992 .

[8] Carlos F. Borges,et al. Parallel Divide and Conquer Algorithms for the Symmetric Tridiagonal Eigenproblem and Bidiagonal Singular Value Problem , 1993 .

[9] J. Barlow. Error analysis of update methods for the symmetric eigenvalue problem , 1993 .

[10] S. Eisenstat,et al. A Stable and Efficient Algorithm for the Rank-One Modification of the Symmetric Eigenproblem , 1994, SIAM J. Matrix Anal. Appl..

[11] Jack J. Dongarra,et al. A fully parallel algorithm for the symmetric eigenvalue problem , 1985, PPSC.