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[求助]
求助翻译下边这段话，谢谢
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| 从单自变量n次插值的推导过程可见：由加权平均法推导得到的关于加权系数的线性方程组（式16）比前述直接求解多项式系数的线性方程组（式2）形式上要规范，式（16）的系数矩阵和增广矩阵具有统一的形式，易于利用克莱姆法则推导得到加权系数，进而得到插值多项式 ，从而有效地避免了拉格朗日插值方法反复构造插值基函数的步骤上的繁琐，也有效地避免了直接求解关于多项式系数的线性方程组（式2）的过程上的复杂，从而使单自变量的插值多项式的推导过程大大简化。同时，该方法由于具有清晰的物理意义，因而可以推广到两自变量乃至多自变量的插值场合，这是拉格朗日方法所难以做到的。 |
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| From a single argument n times the interpolation process is derived can be seen: from the weighted average method to be derived on the weighted coefficient of linear equations (Type 16) than the aforementioned directly solve polynomial coefficient of linear equations (2) in the form of To the norms, the type (16) of the matrix and broaden matrix in the form of a unified, easy-to-use rules derived Cramer has been weighted coefficient, which has been polynomial interpolation, so as to effectively prevent the Lagrange interpolation Construction methods repeatedly interpolation basis function on the steps of the red tape, but also effectively avoid direct on solving polynomial coefficient of linear equations (2) on the complexity of the process, so that a single variable interpolation of a number of -Derived greatly simplify the process. At the same time, as a result of this method has clear physical meaning, which can be extended to two independent variables, and even more variable interpolation of occasions, this is the Lagrangian approach can not achieve. |
2楼2008-10-16 11:20:51
3楼2008-10-16 13:40:45
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From a single argument n times the interpolation process is derived can be seen: from the weighted average method to be derived on the weighted coefficient of linear equations (Type 16) than the aforementioned directly solve polynomial coefficient of linear equations (2) in the form of To the norms, the type (16) of the matrix and broaden matrix in the form of a unified, easy-to-use rules derived Cramer has been weighted coefficient, which has been polynomial interpolation, so as to effectively prevent the Lagrange interpolation Construction methods repeatedly interpolation basis function on the steps of the red tape, but also effectively avoid direct on solving polynomial coefficient of linear equations (2) on the complexity of the process, so that a single variable interpolation of a number of -Derived greatly simplify the process. At the same time, as a result of this method has clear physical meaning, which can be extended to two independent variables, and even more variable interpolation of occasions, this is the Lagrangian approach can not achieve. 这是在线翻译的，不好 |
4楼2008-10-16 17:08:57