Scholarlink

<p>This paper presents a new computational approach designed to tackle the challenges posed by approximation theory. The approach revolves around utilizing pseudo-Chebyshev wavelet approximations, a concept pioneered by Lal et al. (Carpathian Math Publ 14(1):29–48, 2022) which based on pseudo-Chebyshev wavelets approximation method. The paper thoroughly outlines the methodology, accompanied by an assessment of error for a specified function. To demonstrate the effectiveness and efficiency of the pseudo-Chebyshev wavelet approximation technique, we present a comparative analysis with the Chebyshev wavelet. Significant findings are illustrated through examples to highlight the advantages of the proposed method. Moreover, the paper derives the error of a function related to function of Hölder class of order <InlineEquation ID="IEq1"> <EquationSource Format="TEX">\(\alpha \)</EquationSource> </InlineEquation> &#xa0; using pseudo-Chebyshev wavelets via orthogonal projection operators, establishing these estimators as notably more precise and theoretically optimal in the realm of wavelet analysis.</p>

错误：搜索内容不能为空，请输入英文关键词
错误：关键词超出字数限制，请精简
高级检索

An Approximated Error of Functions of Hölder Class by Pseudo-Chebyshev Wavelet Method Using Orthogonal Projection Operator

  • 期刊论文

  • 发表日期：

    2025年10月8日

查看全文
  • Susheel Kumar,
  • Sudhir Kumar Mishra,
  • Gaurav Kumar Mishra,
  • Lakshmi Narayan Mishra,
  • Laxmi Rathour

摘要

This paper presents a new computational approach designed to tackle the challenges posed by approximation theory. The approach revolves around utilizing pseudo-Chebyshev wavelet approximations, a concept pioneered by Lal et al. (Carpathian Math Publ 14(1):29–48, 2022) which based on pseudo-Chebyshev wavelets approximation method. The paper thoroughly outlines the methodology, accompanied by an assessment of error for a specified function. To demonstrate the effectiveness and efficiency of the pseudo-Chebyshev wavelet approximation technique, we present a comparative analysis with the Chebyshev wavelet. Significant findings are illustrated through examples to highlight the advantages of the proposed method. Moreover, the paper derives the error of a function related to function of Hölder class of order \(\alpha \)   using pseudo-Chebyshev wavelets via orthogonal projection operators, establishing these estimators as notably more precise and theoretically optimal in the realm of wavelet analysis.