On the Numerical Solutions of Ill-Posed Problems

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 ill-posed problems. Also, we present one of the traditional stable method for solving linear ill-posed problems, this method called Tikhonov or variational regularization method. Comparison between the two methods is one of the main goals of this book. This book is highly recommended to both postgraduate students and researchers in wide variety of applications.