简介:TherestartedFOMmethodpresentedbySimoncini[7]accordingtothenaturalcollinearityofallresidualsisanefficientmethodforsolvingshiftedsystems,whichgeneratesthesameKrylovsubspacewhentheshiftsarehandledsimultaneously.However,restartingslowsdowntheconvergence.WepresentapracticalmethodforsolvingtheshiftedsystemsbyaddingsomeRitzvectorsintotheKrylovsubspacetoformanaugmentedKrylovsubspace.NumericalexperimentsillustratethattheaugmentedFOMapproach(restartedversion)canconvergemorequicklythantherestartedFOMmethod.