In this paper, we consider the linearly structured partial polynomial inverse eigenvalue problem (LPPIEP) of constructing matrices Ai∈Rn×n for i=0,1,2,…,(k−1) specified linear structure such that matrix P(λ)=λkIn+∑i=0k−1λiAi has m (1⩽m⩽kn) prescribed eigenpairs as its eigenvalues and eigenvectors. Many practical applications give rise to polynomials. Typical are symmetric, skew-symmetric, tridi...

The affine inverse eigenvalue problem consists of identifying a real symmetric matrix with prescribed set eigenvalues in an space. Due to its ubiquity applications, various instances the have been widely studied literature. Previous algorithmic solutions were typically nonconvex heuristics and often developed case-by-case manner for specific structured spaces. In this short note we describe gen...

<p style='text-indent:20px;'>A discrete analog is considered for the inverse transmission eigenvalue problem, having applications in acoustics. We provide a well-posed problem statement, develop constructive procedure solving this prove uniqueness of solution, global solvability, local and stability. Our approach based on reduction to linear system with polynomials spectral parameter boun...