§4分段低次插值 piecewise polynomial approximation 例:在-5,5上考察f(x)= 1+x 的Ln(x)。取x=-5+10;(i=0,…,m Lnx)冷f(x) Remember what I hav aid? Increasing the degree of interpo polynomial will NoT guaranted a good ru shce high-degree polynomial n越大, 05 oscillating 端点附近抖动 越大,称为 Runge现象 分段低次插值§4 分段低次插值 /* piecewise polynomial approximation */ Remember what I have said? Increasing the degree of interpolating polynomial will NOT guarantee a good result, since high-degree polynomials are oscillating. 例：在[5, 5]上考察 的Ln 2 (x)。取 1 1 ( ) x f x   ( 0, ..., ) 10 5 i i n n xi     -5 -4 -3 -2 -1 0 1 2 3 4 5 -0.5 0 0.5 1 1.5 2 2.5 n 越大， 端点附近抖动 越大，称为 Runge 现象 Ln (x)  f (x) 分段低次插值