插值与拟合-----外文翻译.doc

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.
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。