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三次样条插值三转角法（m 法）——以一阶导数为参数

Cubic Spline Interpolation With Three Rotation Angles (m Method) —Taking the First Derivative as a Parameter

Applied Mathematics Information / 2021,3(4): 1-21 / 2021-12-14 772 1300

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• Authors: 刘大海
• Information:

  1．深圳市地质局 深圳；
  2．深圳地质建设工程公司；深圳

• Keywords:
  Cubic spline; Interpolation; Three angle method; m method; Computational mathematics; Equations; Solving
  三次样条; 插值; 三转角法; m 法; 计算数学; 方程组; 求解
• Abstract: Cubic spline interpolation has important applications in engineering. Generally, there are two methods to establish spline interpolation: the three rotation method with the first derivative as the parameter (m method) and the three bending moment method with the second derivative as the parameter (M method). When the interpolation node equations are established, the m method is more simple to deal with the first kind of boundary conditions, and the M method is more convenient to deal with the second kind of boundary conditions. In order to facilitate the calculation programming, the establishment and solution of the nodal equations of cubic spline interpolation three rotation method (m method) are derived in this paper. 三次样条插值在工程中有重要应用。通常，建立样条插值的方法有2 种：以一阶导数为参数的三转角法（m 法）及以二阶导数为参数的三弯矩法（M 法）。在建立插值节点方程组时，m 法对第1 类边界条件的处理较为简洁，M 法对第2 类边界条件的处理较为便捷。为方便计算编程，本文全面整理、详细补充导出了三次样条插值三转角法（m 法）节点方程组的建立及其求解方法。
• DOI: 10.35534/ami.0304002
• Cite: 刘大海．三次样条插值三转角法（m 法）——以一阶导数为参数［J］．应用数学资讯，2021，3（4）：1-21．