Example 4. 11. Compute P3(2.5)in Example 1.10 using nested multipli- cation Using(1.59), we write P3(x)=(-0.1(x-4)+0.5)(x-3)-2)(x-1)+5 The values in(1.60)are 0.1 S2=-0.1(25-4)+05=0.65 S1=0.65(25-3)-2=-2325 S0=-2325(25-1)+5=1.5125 Therefore, P3(2.5)=1.5125
Definition 4.1(Divided Differences). The divided differences for a func tion f(a)are defined as follows k f{xk-1,m」 f[=k-flack-1 Ck-Ik_1 7 f k-2, k-1, CkI flrk-1 Ik]-f ak-2, Tk-1 (1.66) k一k-2 k-3k=2、k-1Ok≈k=2k-1-和=3x=2b-1 The recursive rule for constructing higher-order divided differenc k-+1,…,÷2 k-j+1 ·· x小-f{xk-j k-1 and is used to construct the divided differences in table 4.8