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.
我們能夠運(yùn)用這個公式直接得到給定函數(shù)f(x)的近似多項(xiàng)式估計(jì)，沒有必要采取拉格朗日或牛頓多項(xiàng)式。給定一個函數(shù)、多項(xiàng)式次數(shù)以及區(qū)間的左右邊界點(diǎn)，上面提到的MATLAB程序“cheby()”可以利用這個公式得到切比雪夫近似多項(xiàng)式。
以下的例子闡述了利用這個公式得到的相同的近似多項(xiàng)式，也可以利用切比雪夫節(jié)點(diǎn)的牛頓多項(xiàng)式得到。