Ill-posed problem has been steadily and surely gaining popularity in mathematical literature for many years. It occurs in a wide variety of applications such as geophysics, astrometry, mathematical biology, and image restoration. The notion of a well-posed problem and ill-posed problem goes back to a famous paper by Jacques Hadamard published in 1902. In many science and engineering applications it is necessary to compute an approximate solution of the linear system. In this work, we present and analyze a recent method called dynamical systems method (DSM) for a stable solution of linear...