Several recovery techniques for parallel iterative methods are presented. First, the implementation of checkpoints in parallel iterative methods is described and analyzed. Then, a simple checkpoint-free faulttolerant scheme for parallel iterative methods, the lossy approach, is presented. When one processor fails and all its data is lost, the system is recovered by computing a new approximate solution using the data of the non-failed processors. The iterative method is then restarted with this new vector. The main advantage of the lossy approach over standard checkpoint algorithms is that it does not increase the computational cost of the iterative solver, when no failure occurs. Experiments are presented that compare the different techniques. The fault tolerant FT-MPI library is used. Both iterative linear solvers and eigensolvers are considered.