  We study the inverse eigenvalue problem for finding doubly stochastic
matrices with specified eigenvalues. By making use of a combination of
Dykstra's algorithm and an alternating projection process onto a non-convex
set, we derive hybrid algorithms for finding doubly stochastic matrices and
symmetric doubly stochastic matrices with prescribed eigenvalues. Furthermore,
we prove that the proposed algorithms converge and linear convergence is also
proved. Numerical examples are presented to demonstrate the efficiency of our
method.
