Convergence of a modified iterated Lavrentiev scheme under weaker assumptions
Abstract
Inverse problems commonly arise in various scientific and engineering applications and are known for their instability with respect to data perturbations, making their numerical treatment both delicate and mathematically demanding. Lavrentiev regularization, particularly its iterative form, is a widely used
technique for solving such problems, especially those governed by monotone operators. However, the classical iterative Lavrentiev method requires the computation of the Frechet derivative at each iteration step, which is
computationally expensive and often depends on strong assumptions for convergence analysis. In this study,
we propose a simplified variant of the iterative Lavrentiev scheme, in which the Fr´echet derivative is computed
only once at the initial approximation u0. We establish convergence and derive error estimates under a relaxed nonlinear condition that is weaker than those typically assumed in the literature. Numerical experiments are
presented to confirm the practical applicability of the method.
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