Processing of experimental curves by applying a regularized double period method

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• 作者：A. A. Belov ; N. N. Kalitkin
• 刊名：Doklady Mathematics
• 出版年：2016
• 出版时间：September 2016
• 年：2016
• 卷：94
• 期：2
• 页码：602-606
• 全文大小：331 KB
• 刊物类别：Mathematics and Statistics
• 刊物主题：Mathematics
  Mathematics
  Russian Library of Science
  
• 出版者：MAIK Nauka/Interperiodica distributed exclusively by Springer Science+Business Media LLC.
• ISSN：1531-8362
• 卷排序：94

文摘

In physical and engineering applications, an important task is the processing of experimental curves measured with considerable errors. Such problems are solved by applying the regularization method, in which success relies heavily on the researcher’s intuition. We propose using an approximation based on the double period method designed for smooth aperiodic functions. Regularization makes use of a Tikhonov stabilizer with the second derivative squared. As a result, the spurious oscillations are suppressed and the shape of an experimental curve is well approximated. This approach makes it possible to solve broad classes of problems in a unified manner. The method is demonstrated as applied to the approximation of cross sections of nuclear reactions important for controlled thermonuclear fusion. Tables recommended as reference data are obtained.