Abstract
Necessary and sufficient conditions are completely characterized for the existence of a positive definite or positive semidefinite solution to the symmetric recursive inverse eigenvalue problem (SRIEP). When a prior (indefinite) solution A to the SRIEP is known, positive definite/semidefinite solutions are formulated in terms of A and basis matrices of the column space of the given recursive matrix R and the null space of RT. Taking into account some computational concerns, an algorithm is proposed that can check whether the SRIEP has a positive definite/semidefinite solution and find such a solution if it exists. Several numerical experiments are given to illustrate the performance of the algorithm.
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