  We present a new Krylov subspace recycling method for solving a linear system
of equations, or a sequence of slowly changing linear systems. Our new method,
named GMRES-SDR, combines randomized sketching and deflated restarting in a way
that avoids orthogononalizing a full Krylov basis. We provide new theory which
characterizes sketched GMRES with and without augmentation as a projection
method using a semi-inner product. We present results of numerical experiments
demonstrating the effectiveness of GMRES-SDR over competitor methods such as
GMRES-DR and GCRO-DR.
