Some non-standard regularizing algorithms and their numerical realization

Abstract

1. Considerable experience has noi been accumulated on the numerical solution of operator equations of the 1st kind. which represent typical examples of ill-posed problems. The main advances have been achieved b>, using regularizing algorithms (r.a.). A detailed theory of the construction of r.a. has be-n developed, and the properties of wide classes of r.a. have been studied theoretically. In the numerical analysis of ill-posed problems, however, the r.a. based sn the Tikhonov parametric functlonal has? until recently, mainly been used, and the only essential difference between concrete r.a.s is in the method of fixing the parameter (by a quasi-optimal method, or on the basis of a discrepant!,. or a priori, etc.) [ 1 ] , The success achieved by practical application of these r.a.s is well knoa-n. On the other hand. nea’ mathematical models, leading to ill-posed problems. are continualI> being introduced into research. and the demands for reliable solutions are al\~a~~s increasing with the result thai ne r.a.s. differing from the standard Tikhonov type. are beginning to look promising for practical use [ 11.