The authors propose a recycling Krylov subspace method for the solution of a
sequence of self-adjoint linear systems. Such problems appear, for example, in
the Newton process for solving nonlinear equations. Ritz vectors are
automatically extracted from one MINRES run and then used for self-adjoint
deflation in the next. The method is designed to work with arbitrary inner
products and arbitrary self-adjoint positive-definite preconditioners whose
inverse can be computed with high accuracy. Numerical experiments with
nonlinear Schr\"odinger equations indicate a substantial decrease in
computation time when recycling is used