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<p>In this paper, we set out to explore a class of operators satisfying the condition <InlineEquation ID="IEq4"> <EquationSource Format="TEX">\(L_2\)</EquationSource> <EquationSource Format="MATHML"><math> <msub> <mi>L</mi> <mn>2</mn> </msub> </math></EquationSource> </InlineEquation>, and check for their Fejér monotone convergence, and weak convergence. Moreover, qualitative studies related to a stability and data dependence analysis are presented. Meaningful comparisons with other numerical algorithms are provided, from the point of view of the convergence speed or CPU time. Additionally, a polynomiographic study is carried out to visually and quantitatively showcase how efficiently the proposed iterative process works.</p>

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On Thakur iteration for \(L_2\)-operators with qualitative analysis

  • 期刊论文

  • 出版模式：

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  • 发表日期：

    2026年3月3日

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  • Cristian Ciobanescu,
  • Alexandru Gogoasa

摘要

In this paper, we set out to explore a class of operators satisfying the condition \(L_2\) L 2 , and check for their Fejér monotone convergence, and weak convergence. Moreover, qualitative studies related to a stability and data dependence analysis are presented. Meaningful comparisons with other numerical algorithms are provided, from the point of view of the convergence speed or CPU time. Additionally, a polynomiographic study is carried out to visually and quantitatively showcase how efficiently the proposed iterative process works.