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<p>A priori parameter choice rules are successful in verifying the convergence of the reconstructed solutions. However, they suffer from a major drawback of utilizing source conditions, which, in most cases, is unknown. This pitfall is circumvented by invoking a posteriori parameter choice rules. In this article, we propound and investigate an Engl-type discrepancy principle for the choice of the regularization parameter <InlineEquation ID="IEq1"> <EquationSource Format="TEX">\(\beta \)</EquationSource> </InlineEquation> in the learning theory perspective and establish the convergence rate. The consistency of the algorithm is an easy consequence. Moreover, we provide some insightful discussion on the weighted parameter <InlineEquation ID="IEq2"> <EquationSource Format="TEX">\(\alpha \)</EquationSource> </InlineEquation>. From a practical point of view, we demonstrate our theoretical analysis through two well-studied academic examples in learning theory.</p>

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A class of parameter choice rules for weighted Tikhonov regularization scheme in learning theory

  • 期刊论文

  • 发表日期：

    2025年9月9日

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  • P. Sreepriya,
  • K. D. Denny,
  • G. D. Reddy

摘要

A priori parameter choice rules are successful in verifying the convergence of the reconstructed solutions. However, they suffer from a major drawback of utilizing source conditions, which, in most cases, is unknown. This pitfall is circumvented by invoking a posteriori parameter choice rules. In this article, we propound and investigate an Engl-type discrepancy principle for the choice of the regularization parameter \(\beta \) in the learning theory perspective and establish the convergence rate. The consistency of the algorithm is an easy consequence. Moreover, we provide some insightful discussion on the weighted parameter \(\alpha \) . From a practical point of view, we demonstrate our theoretical analysis through two well-studied academic examples in learning theory.