Using Tikhonov Regularization Method to Solve the Hamiltonian in an Inverse Problem for a Quantum Spin System

Tikhonov regularization is a popular method for solving linear discrete ill-posed problems. This method can conveniently solve small-scale problems with the aid of the generalized singular value decomposition. However, it is impractical to use this decomposition for large-scale problems. We develop a new matrix decomposition method that are well suited for the solution of large-scale problems. This method can be applied to the inverse problem where we are given a set of desired orthogonal wave functions and we are trying to construct the parent Hamiltonian for a quantum spin system.