On the Nonmonotone Behavior of the Newton-Gmback Method

GMBACK is a Krylov solver for large linear systems, which is based on backward error minimization properties. The minimum backward error is guaranteed (in exact arithmetic) to decrease when the subspace dimension is increased. In this paper we consider two test problems which lead to nonlinear systems which we solve by the Newton-GMBACK. We notice that in floating point arithmetic the mentioned property does not longer hold; this leads to nonmonotone behavior of the errors, as reported in a previous paper. We also propose a remedy, which solves this drawback.