May 28, 2026Russian Mathematics0 citations

Convergence Rate Estimates for an Iteratively Regularized Gradient Method with an a Posteriori Stopping Rule

Q: What does this research mean for the field?

An iteratively regularized gradient method with an a posteriori stopping rule achieves a specific accuracy estimate based on input data error levels for solving nonlinear irregular operator equations in Hilbert spaces, without requiring structural conditions on the operator. Novelty: ClaimNovelty.METHODOLOGICAL. Consensus alignment: ConsensusAlignment.NEUTRAL.

MKM. M. Kokurin

Key Points

The aim is to establish accuracy estimates for an iteratively regularized gradient method in solving nonlinear operations.
Utilized an iteratively regularized gradient method with a posteriori stopping rule.
Assumed solutions satisfy a sourcewise condition without structural operator restrictions.
Established an accuracy estimate based on the error level of input data for the proposed method.

Abstract

We study an iteratively regularized gradient method with an a posteriori stopping rule for solving nonlinear irregular operator equations in Hilbert spaces. An accuracy estimate in terms of the error level of input data for this method is established. We assume that the desired solution satisfies a sourcewise condition, and we use no structural conditions on the operator of the problem.

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