An approach to solving inverse eigenvalue problems for matrices

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.