On optimization of projection methods for solving some classes of severely ill-posed problems

Abstract

In the present paper, the issue of the optimal solving severely ill-posed problems is studied. The authors proposed projection scheme of discretization which is efficient with respect to the amount of used Galerkin information. By this scheme, the order-optimal estimates of quantities described information and algorithmic complexity are achieved.

Keywords:

• severely ill-posed problems
• Galerkin information
• minimal radius
• information complexity
• algorithmic complexity

AMS Subject Classifications:

• 65R20
• 47A52

Notes

No potential conflict of interest was reported by the authors.