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An iterative algorithm for state determination is presented that uses asphysical input the probability distributions for the eigenvalues of two or moreobservables in an unknown state $\Phi$. Starting form an arbitrary state$\Psi_{0}$, a succession of states $\Psi_{n}$ is obtained that converges to$\Phi$ or to a Pauli partner. This algorithm for state reconstruction isefficient and robust as is seen in the numerical tests presented and is auseful tool not only for state determination but also for the study of Paulipartners. Its main ingredient is the Physical Imposition Operator that changesany state to have the same physical properties, with respect to an observable,of another state.

State determination: an iterative algorithm