For multiple applications, such as improving post bonding wafer overlay, we are looking for a least squares solver method that solves for a matrix under the constraint of being symmetric and being two-side bounded. This is also referred to in literature as the symmetric Procrustes problem. The solution for the unbounded Procrustes problem is known and can be solver using the singular value decomposition. For the single-bounded (positive semidefinite) problem in many cases a (bounded) solution does not exist. For the double bounded problem a solution should always exist, but no literature was found on this. We are looking for clever mathematical tricks to directly solve the problem, but if that is not possible, numerical/iterative optimization algorithms may also be considered.