Inverse eigenvalue problems associated with spring-mass systems
The authors establish necessary and sufficient conditions for the existence of unique Jacobi matrices \(T_{1,j}\) and \(T_{j+1,n}\), of orders \(j\times j\) and \((n-j)\times (n-j)\) respectively, such that \(T_{1,j}\), \(T_{j+1,n}\) and a certain rank one perturbation of \(T_{1,j}\oplus T_{j+1,n}\) have specified eigenvalues. They also examine the implications for ideal spring-mass systems of this result and of some related known results on inverse eigenvalue problems for Jacobi matrices.
scientific article; zbMATH DE number 1000062
scientific article