Twodynamicalsystemmethodsarestudiedforsolvinglinearill-posedproblemswithbothoperatorandright-handnonexact.ThemethodssolveaCauchyproblemforalinearoperatorequationwhichpossessesaglobalsolution.Thelimitoftheglobalsolutionatinfinitysolvestheoriginallinearequation.Moreover,wealsopresentaconvergentiterativeprocessforsolvingtheCauchyproblem.