Tanana

Methods for Solving Operator Equ Tanana 1st edition

This monograph investigates the methods for solving linear operator equations from the viewpoint of their stability relative to disturbance of the initial information. It focuses on the operation equations: au=f, where u, f are desired and given elements of certain metric spaces (U and F respectively), and A is a given operator acting from U unto F. The concept of an optimum to a method for solving the equation Au=f with an approximately given operator is introduced and an analysis of the method from the viewpoint of their optimums is pursued. Problems of regularizing operator equations with a disturbance in the operator are considered. General schemes for finite-dimensional approximation of regularized solutions are also formulated and investigated.