Three-layer Iterative Solution Procedure Ill-posed Equations of the First Kind in a Hilbert Space
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Abstract
To solve linear operator equations of the first kind with a positive bounded self-adjoint operator in a Hilbert space an explicit three-layer iterative procedure is proposed. The convergence of the iterative method is studied in the case of a priori and a posteriori choice of the regularization parameter for the exact and approximate right-hand sides of the operator equation in the original norm of the Hilbert space. The convergence of the iteration method has been proven in the semi-norm of a Hilbert space. The proposed method solves the numerical model problem. The results obtained can be used in theoretical research in solving linear operator equations, as well as in solving applied ill-posed problems.
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References
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