Positive interpolation by trigonometric functions

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• 作者：Maria Hussain ; Mubashrah Saddiqa
• 关键词：Trigonometric functions ; Positive interpolation ; Free parameters ; Error estimation ; 68U05 ; 65D05 ; 65D07 ; 65D18
• 刊名：Afrika Matematika
• 出版年：2016
• 出版时间：March 2016
• 年：2016
• 卷：27
• 期：1-2
• 页码：239-262
• 全文大小：5,371 KB
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• 作者单位：Maria Hussain (1)
  Mubashrah Saddiqa (1)
  
  1. Department of Mathematics, Lahore College for Women University, Lahore, Pakistan
  
• 刊物类别：Mathematics and Statistics
• 刊物主题：Mathematics Education
  Applications of Mathematics
  History of Mathematics
  Mathematics
  
• 出版者：Springer Berlin / Heidelberg
• ISSN：2190-7668

文摘

A \(C^1\) rational quadratic trigonometric interpolating function with three parameters is developed. The order of approximation of the developed \(C^1\) trigonometric interpolant is \(O( {h_i^2 })\). The \(C^1\) rational quadratic trigonometric function is extended to a \(C^1\) bivariate rational quadratic trigonometric function. The developed \(C^1\) bivariate trigonometric interpolant has six parameters in each rectangular patch. Automatic selection schemes for parameters are developed to preserve the positive shape of curve and surface data using \(C^1\) rational quadratic trigonometric function and \(C^1\) bivariate rational quadratic trigonometric function respectively. Performing the result, it is noticed that developed positivity preserving interpolation schemes are fast, efficient and well suited for all data types. Several numerical examples are presented to ascertain the correctness and usability of developed schemes. Keywords Trigonometric functions Positive interpolation Free parameters Error estimation