Some Inverse Eigenproblems for Jacobi and Arrow Matrices
Borges, Carlos F.
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We consider the problem of reconstruction 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.
The first and third authors were supported by direct grant from the Naval Postgraduate School. The third author also acknowledges support from the Interdisciplinary Project Center for Supercomputing at the ETH, Zurich.The article of record as published may be found at DOI: 10.1002/nla.1680020302