Regularization Methods for Solution of Linear Systems

The advent of the computer had forced the application of mathematics to all branches of human endeavor. One important property of mathematical problems is the stability of their solutions to small changes in the initial data. Problems that f il to satisfy this stability condition are called ill-posed. If the initial data in such problems are known only approximately and contain a random error, then the above mentioned instability of their solutions leads to non-uniqueness of the classically derived approximate solutions and to serious difficulties in their physical interpretation. In solving such problems, one must first define the concept of an approximate solution that is stable to small changes in the initial data, and to use special methods for deriving this solution. We are working in the development of the regularization method in the construction of approximate solutions of ill-posed problems