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Some inverse eigenproblems for Jacobi and arrow matrices
Author(s) -
Borges Carlos F.,
Frezza Ruggero,
Gragg William B.
Publication year - 1995
Publication title -
numerical linear algebra with applications
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 1.02
H-Index - 53
eISSN - 1099-1506
pISSN - 1070-5325
DOI - 10.1002/nla.1680020302
Subject(s) - mathematics , tridiagonal matrix , singular value decomposition , inverse , matrix (chemical analysis) , jacobi method , singular value , algebra over a field , jacobi eigenvalue algorithm , algorithm , pure mathematics , eigenvalues and eigenvectors , geometry , physics , materials science , quantum mechanics , composite material
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.