I am solving an IEP but the form of the problem and the constraints is such that it has not unique solution. It may have many different solutions. I would like to know is there any problem if such thing happens?
Update
I am solving the problem of producing a matrix $A$ whose off-diagonal entries are correspond to the Wheel graph by the given eigenvalues $\lambda = \{\lambda_1, \lambda_2, \cdots , \lambda_n\}$ and vector $X$ such that $\lambda_i$ is an eigenvalue of $A_i$ where $A_i$ is the $i$th leading principal submatrix of $A$ and $X$ is an eigenvector of $A$.
I solved this problem for Path graph with unique solution but for Wheel graph the given information doesn't produce a unique solution.
If any entry of the $A$ is given as input, then the problem will have unique solution
But I think it is not a good idea to ask user to give one of the entries !