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Methods for Solving Operator Equations
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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.
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