插值与拟合--------外文翻译.doc

PADE APPROXIMATION BY RATIONAL FUNCTION 129
We can apply this formula to get the polynomial approximation directly for
a given function f (x), without having to resort to the Lagrange or Newton
polynomial. Given a function, the degree of the approximate polynomial, and the
left/right boundary points of the interval, the above MATLAB routine “cheby()”
uses this formula to make the Chebyshev polynomial approximation.
The following example illustrates that this formula gives the same approximate
polynomial function as could be obtained by applying the Newton polynomial
with the Chebyshev nodes.
Example 3.1. Approximation by Chebyshev Polynomial. Consider the problem
of finding the second-degree (N = 2) polynomial to approximate the function
. We make the following program “do_cheby.m”, which uses
the MATLAB routine “cheby()” for this job and uses Lagrange/Newton polynomial
with the Chebyshev nodes to do the same job. Readers can run this program
to check if the results are the same.



插值与拟合
我们能够运用这个公式直接得到给定函数f(x)的近似多项式估计，没有必要采取拉格朗日或牛顿多项式。给定一个函数、多项式次数以及区间的左右边界点，上面提到的MATLAB程序“cheby()”可以利用这个公式得到切比雪夫近似多项式。
以下的例子阐述了利用这个公式得到的相同的近似多项式，也可以利用切比雪夫节点的牛顿多项式得到。
例3.1．切比雪夫多项式近似值。考虑找到函数
的二阶多项式估计。写出以下程序“do_cheby.m”，这个程序运用了MATLAB程序“cheby()”解决这个问题，并且运用了切比雪夫节点的牛顿或拉格朗日多项式来解决相同的问题，读者可以运行这个程序，检查结果是否相同。