| 散乱数据(2m-1,2n-1)次多项式自然样条插值 |
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| 引用本文： | 许伟志,关履泰,韩乐.散乱数据(2m-1,2n-1)次多项式自然样条插值[J].数值计算与计算机应用,2009,30(4). |
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| 作者姓名： | 许伟志 关履泰 韩乐 |
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| 作者单位： | 1. SYSU,中山大学,科学计算与计算机应用系,广州,510275
2. SCUT,华南理工大学,理学院,广州,510640 |
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| 基金项目： | 教育部高等学校博士点科研基金 |
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| 摘 要： | 考虑对窄间散乱数据(2m-1,2n-1)次多项式自然样条插值,使得插值函数对x的m次偏导数和对y的n次偏导数平方积分极小(带自然边界条件).用希尔伯特空间样条方法,得出其解的结构,解的系数能够用线性方程组确定,方程组系数矩阵对称,可用改进的平方根法解.例子表明方法简单,效果良好.
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| 关 键 词： | 散乱数据捕值 (2m-1 2n-1)次多项式 自然样条 |
INTERPOLATION FOR SCATTERED DATA BY (2m-1, 2n-1) DEGREE POLYNOMIAL NATURAL SPLINES |
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| Xu Weizhi,Guan Lvtai,Han Le.INTERPOLATION FOR SCATTERED DATA BY (2m-1, 2n-1) DEGREE POLYNOMIAL NATURAL SPLINES[J].Journal on Numerical Methods and Computer Applications,2009,30(4). |
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| Authors: | Xu Weizhi Guan Lvtai Han Le |
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| Abstract: | (2m- 1, 2n - 1) degree polynomial natural splines interpolations for space scattered data such that the integral of square of partial derivative of m orders to x and n orders to y for the interpolating function is minimal(with natural boundary conditions). The solution is constructed as the sum of a (m - 1, n - 1) degree polynomial and piecewise (2m - 1, 2n - 1) degree polynomial by Hilbert space spline function methods. Its coefficients can be decided by a linear system. The coefficient matrix is so symmetry that the improved square root method can be successed. Results are very simple and can be achieved easily in computer programs. |
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| Keywords: | scattered data interpolation polynomial of degree (2m-1 2n-1) natural spline |
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