论文标题
关于带帕德近似值的回归分析
On regression analysis with Padé approximants
论文作者
论文摘要
讨论了将Padé近似值应用于二维回归分析的优势和困难。在最小二乘方法中建议了残留物的新表述。在有理功能的情况下，它导致线性方程式系统。在这种方法中，证明了使用Tikhonov正则化技术避免过度拟合的可能性。为了说明建议方法的效率，考虑了物理学和可靠性理论的几个实际情况。
The advantages and difficulties of application of Padé approximants to two-dimensional regression analysis are discussed. New formulation of residuals is suggested in the method of least squares. It leads to a system of linear equations in case of rational functions. The possibility of using Tikhonov regularization technique to avoid overfitting is demonstrated in this approach. To illustrate the efficiency of the suggested method, several practical cases from physics and reliability theory are considered.
