Geodesic
An approach to solving inverse eigenvalue problems for matrices
Zapiski Nauchnykh Seminarov POMI, Computational methods and algorithms. Part XIV, Tome 268 (2000), pp. 95-114

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The paper considers different formulations of inverse eigenvalue problems for matrices whose entries either polynomially or rationally depend on unknown parameters. An approach to solving inverse problems together with numerical algorithms is suggested. The solution of inverse problems is reduced to the problem of finding the so-called discrete solutions of nonlinear algebraic systems. The corresponding systems are constructed using the trace method, and their discrete roots are found by applying the algorithms for solving nonlinear algebraic systems in several variables previously suggested by the author. 
@article{ZNSL_2000_268_a6,
     author = {V. N. Kublanovskaya},
     title = {An approach to solving inverse eigenvalue problems for matrices},
     journal = {Zapiski Nauchnykh Seminarov POMI},
     pages = {95--114},
     publisher = {mathdoc},
     volume = {268},
     year = {2000},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/ZNSL_2000_268_a6/}
}
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V. N. Kublanovskaya. An approach to solving inverse eigenvalue problems for matrices. Zapiski Nauchnykh Seminarov POMI, Computational methods and algorithms. Part XIV, Tome 268 (2000), pp. 95-114. http://geodesic.mathdoc.fr/item/ZNSL_2000_268_a6/