In \u00a0this \u00a0paper \u00a0an \u00a0interesting \u00a0property \u00a0of \u00a0the \u00a0restarted \u00a0FOM \u00a0algorithm \u00a0for \u00a0solving \u00a0large
nonsymmetric \u00a0linear \u00a0systems \u00a0is \u00a0presented \u00a0and \u00a0studied. \u00a0By \u00a0establishing \u00a0a \u00a0relationship \u00a0between \u00a0the
convergence of its residual vectors and the convergence of Ritz values in the Arnoldi procedure, it is shown
that some important information of previous FOM(m) cycles may be saved by the iteration approximates at
the time of restarting, with which the FOM(m) cycles can complement one another harmoniously in reducing
the \u00a0iteration \u00a0residual. \u00a0Based \u00a0on \u00a0the \u00a0study \u00a0of \u00a0FOM(m), \u00a0two \u00a0polynomial \u00a0preconditioning \u00a0techniques \u00a0are
proposed; \u00a0one \u00a0is \u00a0for \u00a0solving \u00a0nonsymmetric \u00a0linear \u00a0systems \u00a0and \u00a0another \u00a0is \u00a0for \u00a0forming \u00a0an \u00a0effective \u00a0starting
vector in the restarted Arnoldi method for solving nonsymmetric eigenvalue problems.
