To solving inverse eigenvalue problems for parametric matrices
Zapiski Nauchnykh Seminarov POMI, Computational methods and algorithms. Part XIX, Tome 334 (2006), pp. 174-192

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Some statements of inverse eigenvalue problems for one-parameter and multiparameter regular polynomial matrices with linear and nonlinear dependences on spectral parameters are considered. Methods for solving inverse eigenvalue problems based on rank factorization, exhaustion, and reduction to nonlinear equations are proposed.
@article{ZNSL_2006_334_a12,
     author = {V. N. Kublanovskaya and V. B. Khazanov},
     title = {To solving inverse eigenvalue problems for parametric matrices},
     journal = {Zapiski Nauchnykh Seminarov POMI},
     pages = {174--192},
     publisher = {mathdoc},
     volume = {334},
     year = {2006},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/ZNSL_2006_334_a12/}
}
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V. N. Kublanovskaya; V. B. Khazanov. To solving inverse eigenvalue problems for parametric matrices. Zapiski Nauchnykh Seminarov POMI, Computational methods and algorithms. Part XIX, Tome 334 (2006), pp. 174-192. http://geodesic.mathdoc.fr/item/ZNSL_2006_334_a12/