参考文献： https://wenku.baidu.com/view/b6aed86baf1ffc4ffe47ac92.html
#include <bits/stdc++.h> using namespace std; const int maxn = 100; double a[maxn][maxn]; int main () { freopen("in.txt","r",stdin); freopen("out.txt","w",stdout); int n = 19; //int s = 0 ,t = 1,x; //输入x 以及 y 的值 for(int i=0 ; i < n ; i++){ for(int j=0 ; j < 2 ; j++){ cin >> a[i][j]; } }// 读入数据 for(int j=1 ; j < n+1 ; j++){ for(int i=j ; i < n ; i++){ a[i][j+1] = 1.0* (a[i][j] - a[i-1][j]) / (a[i][0] - a[i-j][0]);// + 0.00500000005; } }// 计算均差 printf("输出xi，yi及各阶均差 "); printf(" Xi f(xi) "); for(int i=0 ; i < n ; i++){ cout << i << " "; for(int j=0 ; j < i+2 ; j++){ printf("%11.10lf ",a[i][j]); } cout << endl; }// 打印均差表 printf("输出牛顿插值表达式 "); printf("F%d(x)= ",n); for(int i=0 ; i < n ; i++) { if(i) printf("+ "); printf("%11.10lf",a[i][i+1]); for(int j=0 ; j < i ; j++) printf("(x-%3.2lf)",a[j][0]); if(i == n) break; cout<< endl; } printf(" "); }
0.1 6.54 4.76 5.19 6.65 4.53 9.51 4.99 12.17 2.21 15.23 6.81 17.35 6.10 19.21 8.89 22.15 4.88 23.46 3.72 27.11 3.21 28.81 2.78 29.87 3.58 30.52 2.28 30.99 2.11 32.01 2.47 33.85 2.26 34.91 1.55 37.5 6
1.7 19.89 4.80 24.52 5.98 34.82 8.83 40.54 12.18 37.67 15.21 41.38 17.92 30.00 19.50 19.68 22.23 14.56 24.56 18.86 27.31 17.98 29.11 21.62 29.87 17.98 30.87 14.86 31.51 12.86 32.89 10.96 33.78 8.68 35.71 9.54 37.5 6
输出xi，yi及各阶均差 Xi f(xi) 0 0.1000000000 6.5400000000 1 4.7600000000 5.1900000000 -0.2896995708 2 6.6500000000 4.5300000000 -0.3492063492 -0.0090850043 3 9.5100000000 4.9900000000 0.1608391608 0.1073780021 0.0123765150 4 12.1700000000 2.2100000000 -1.0451127820 -0.2184695549 -0.0439740293 -0.0046686449 5 15.2300000000 6.8100000000 1.5032679739 0.4455211112 0.0773881895 0.0115914249 0.0010746907 6 17.3500000000 6.1000000000 -0.3349056604 -0.3548597749 -0.1020893987 -0.0167736064 -0.0022529810 -0.0001929085 7 19.2100000000 8.8900000000 1.5000000000 0.4610315730 0.1158936574 0.0224724800 0.0031246884 0.0003721571 0.0000295691 8 22.1500000000 4.8800000000 -1.3639455782 -0.5966553288 -0.1528449280 -0.0269277140 -0.0039082432 -0.0004537375 -0.0000474925 -0.0000034949 9 23.4600000000 3.7200000000 -0.8854961832 0.1125763282 0.1160771943 0.0326758350 0.0052793223 0.0006586068 0.0000661716 0.0000060783 0.0000004098 10 27.1100000000 3.2100000000 -0.1397260274 0.1503568863 0.0047823491 -0.0114031604 -0.0037103531 -0.0006017186 -0.0000716094 -0.0000067342 -0.0000005733 -0.0000000364 11 28.8100000000 2.7800000000 -0.2529411765 -0.0211617101 -0.0257535430 -0.0031808221 0.0007174815 0.0003260556 0.0000557557 0.0000065992 0.0000006017 0.0000000489 0.0000000030 12 29.8700000000 3.5800000000 0.7547169811 0.3650935354 0.0602582286 0.0111414212 0.0013435500 0.0000500055 -0.0000188559 -0.0000042153 -0.0000005312 -0.0000000488 -0.0000000039 -0.0000000002 13 30.5200000000 2.2800000000 -2.0000000000 -1.6109456030 -0.5794836183 -0.0906149925 -0.0121572776 -0.0011937071 -0.0000944353 -0.0000049431 -0.0000000397 0.0000000234 0.0000000030 0.0000000003 0.0000000000 14 30.9900000000 2.1100000000 -0.3617021277 1.4627659574 1.4099594314 0.5127430540 0.0801272306 0.0104394240 0.0009875324 0.0000793231 0.0000053468 0.0000002862 0.0000000122 0.0000000004 0.0000000000 -0.0000000000 15 32.0100000000 2.4700000000 0.3529411765 0.4796263786 -0.4594110181 -0.5841782655 -0.2238614938 -0.0355542368 -0.0046646715 -0.0004415784 -0.0000355322 -0.0000024362 -0.0000001372 -0.0000000066 -0.0000000003 -0.0000000000 -0.0000000000 16 33.8500000000 2.2600000000 -0.1141304348 -0.1633117522 -0.1930745138 0.0669187197 0.1291859098 0.0523809204 0.0084634415 0.0011220609 0.0001068060 0.0000086266 0.0000005941 0.0000000337 0.0000000017 0.0000000001 0.0000000000 0.0000000000 17 34.9100000000 1.5500000000 -0.6698113208 -0.1916140986 -0.0072199863 0.0423358832 -0.0048775469 -0.0219776158 -0.0095331457 -0.0015717543 -0.0002111140 -0.0000202497 -0.0000016444 -0.0000001137 -0.0000000065 -0.0000000003 -0.0000000000 -0.0000000000 -0.0000000000 18 37.5000000000 6.0000000000 1.7181467181 0.6542350792 0.1540708885 0.0247758640 -0.0025157621 0.0003095393 0.0025646899 0.0011643730 0.0001948809 0.0000264492 0.0000025532 0.0000002083 0.0000000145 0.0000000008 0.0000000000 0.0000000000 0.0000000000 0.0000000000 输出牛顿插值表达式 F19(x)= 6.5400000000 + -0.2896995708(x-0.10) + -0.0090850043(x-0.10)(x-4.76) + 0.0123765150(x-0.10)(x-4.76)(x-6.65) + -0.0046686449(x-0.10)(x-4.76)(x-6.65)(x-9.51) + 0.0010746907(x-0.10)(x-4.76)(x-6.65)(x-9.51)(x-12.17) + -0.0001929085(x-0.10)(x-4.76)(x-6.65)(x-9.51)(x-12.17)(x-15.23) + 0.0000295691(x-0.10)(x-4.76)(x-6.65)(x-9.51)(x-12.17)(x-15.23)(x-17.35) + -0.0000034949(x-0.10)(x-4.76)(x-6.65)(x-9.51)(x-12.17)(x-15.23)(x-17.35)(x-19.21) + 0.0000004098(x-0.10)(x-4.76)(x-6.65)(x-9.51)(x-12.17)(x-15.23)(x-17.35)(x-19.21)(x-22.15) + -0.0000000364(x-0.10)(x-4.76)(x-6.65)(x-9.51)(x-12.17)(x-15.23)(x-17.35)(x-19.21)(x-22.15)(x-23.46) + 0.0000000030(x-0.10)(x-4.76)(x-6.65)(x-9.51)(x-12.17)(x-15.23)(x-17.35)(x-19.21)(x-22.15)(x-23.46)(x-27.11) + -0.0000000002(x-0.10)(x-4.76)(x-6.65)(x-9.51)(x-12.17)(x-15.23)(x-17.35)(x-19.21)(x-22.15)(x-23.46)(x-27.11)(x-28.81) + 0.0000000000(x-0.10)(x-4.76)(x-6.65)(x-9.51)(x-12.17)(x-15.23)(x-17.35)(x-19.21)(x-22.15)(x-23.46)(x-27.11)(x-28.81)(x-29.87) + -0.0000000000(x-0.10)(x-4.76)(x-6.65)(x-9.51)(x-12.17)(x-15.23)(x-17.35)(x-19.21)(x-22.15)(x-23.46)(x-27.11)(x-28.81)(x-29.87)(x-30.52) + -0.0000000000(x-0.10)(x-4.76)(x-6.65)(x-9.51)(x-12.17)(x-15.23)(x-17.35)(x-19.21)(x-22.15)(x-23.46)(x-27.11)(x-28.81)(x-29.87)(x-30.52)(x-30.99) + 0.0000000000(x-0.10)(x-4.76)(x-6.65)(x-9.51)(x-12.17)(x-15.23)(x-17.35)(x-19.21)(x-22.15)(x-23.46)(x-27.11)(x-28.81)(x-29.87)(x-30.52)(x-30.99)(x-32.01) + -0.0000000000(x-0.10)(x-4.76)(x-6.65)(x-9.51)(x-12.17)(x-15.23)(x-17.35)(x-19.21)(x-22.15)(x-23.46)(x-27.11)(x-28.81)(x-29.87)(x-30.52)(x-30.99)(x-32.01)(x-33.85) + 0.0000000000(x-0.10)(x-4.76)(x-6.65)(x-9.51)(x-12.17)(x-15.23)(x-17.35)(x-19.21)(x-22.15)(x-23.46)(x-27.11)(x-28.81)(x-29.87)(x-30.52)(x-30.99)(x-32.01)(x-33.85)(x-34.91)
输出xi，yi及各阶均差 Xi f(xi) 0 1.70 19.89 1 4.80 24.52 1.49 2 5.98 34.82 8.73 1.69 3 8.83 40.54 2.01 -1.67 -0.47 4 12.18 37.67 -0.86 -0.46 0.16 0.06 5 15.21 41.38 1.22 0.33 0.09 -0.01 -0.01 6 17.92 30.00 -4.20 -0.94 -0.14 -0.02 -0.00 0.00 7 19.50 19.68 -6.53 -0.54 0.05 0.02 0.00 0.00 -0.00 8 22.23 14.56 -1.88 1.08 0.23 0.02 -0.00 -0.00 -0.00 -0.00 9 24.56 18.86 1.85 0.74 -0.05 -0.03 -0.00 -0.00 -0.00 0.00 0.00 10 27.31 17.98 -0.32 -0.43 -0.15 -0.01 0.00 0.00 0.00 0.00 0.00 -0.00 11 29.11 21.62 2.02 0.51 0.14 0.03 0.00 0.00 -0.00 -0.00 -0.00 -0.00 -0.00 12 29.87 17.98 -4.79 -2.66 -0.60 -0.10 -0.01 -0.00 -0.00 -0.00 -0.00 0.00 0.00 0.00 13 30.87 14.86 -3.12 0.95 1.01 0.26 0.04 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 14 31.51 12.86 -3.12 -0.00 -0.40 -0.34 -0.09 -0.01 -0.00 -0.00 -0.00 -0.00 -0.00 -0.00 -0.00 -0.00 15 32.89 10.96 -1.38 0.87 0.29 0.18 0.09 0.02 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 16 33.78 8.68 -2.56 -0.52 -0.48 -0.20 -0.08 -0.03 -0.01 -0.00 -0.00 -0.00 -0.00 -0.00 -0.00 -0.00 -0.00 -0.00 17 35.71 9.54 0.45 1.07 0.38 0.18 0.06 0.02 0.01 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 18 37.50 6.00 -1.98 -0.65 -0.37 -0.13 -0.05 -0.01 -0.00 -0.00 -0.00 -0.00 -0.00 -0.00 -0.00 -0.00 -0.00 -0.00 -0.00 -0.00 输出牛顿插值表达式 F19(x)= 19.89 + 1.49(x-1.70) + 1.69(x-1.70)(x-4.80) + -0.47(x-1.70)(x-4.80)(x-5.98) + 0.06(x-1.70)(x-4.80)(x-5.98)(x-8.83) + -0.01(x-1.70)(x-4.80)(x-5.98)(x-8.83)(x-12.18) + 0.00(x-1.70)(x-4.80)(x-5.98)(x-8.83)(x-12.18)(x-15.21) + -0.00(x-1.70)(x-4.80)(x-5.98)(x-8.83)(x-12.18)(x-15.21)(x-17.92) + -0.00(x-1.70)(x-4.80)(x-5.98)(x-8.83)(x-12.18)(x-15.21)(x-17.92)(x-19.50) + 0.00(x-1.70)(x-4.80)(x-5.98)(x-8.83)(x-12.18)(x-15.21)(x-17.92)(x-19.50)(x-22.23) + -0.00(x-1.70)(x-4.80)(x-5.98)(x-8.83)(x-12.18)(x-15.21)(x-17.92)(x-19.50)(x-22.23)(x-24.56) + -0.00(x-1.70)(x-4.80)(x-5.98)(x-8.83)(x-12.18)(x-15.21)(x-17.92)(x-19.50)(x-22.23)(x-24.56)(x-27.31) + 0.00(x-1.70)(x-4.80)(x-5.98)(x-8.83)(x-12.18)(x-15.21)(x-17.92)(x-19.50)(x-22.23)(x-24.56)(x-27.31)(x-29.11) + 0.00(x-1.70)(x-4.80)(x-5.98)(x-8.83)(x-12.18)(x-15.21)(x-17.92)(x-19.50)(x-22.23)(x-24.56)(x-27.31)(x-29.11)(x-29.87) + -0.00(x-1.70)(x-4.80)(x-5.98)(x-8.83)(x-12.18)(x-15.21)(x-17.92)(x-19.50)(x-22.23)(x-24.56)(x-27.31)(x-29.11)(x-29.87)(x-30.87) + 0.00(x-1.70)(x-4.80)(x-5.98)(x-8.83)(x-12.18)(x-15.21)(x-17.92)(x-19.50)(x-22.23)(x-24.56)(x-27.31)(x-29.11)(x-29.87)(x-30.87)(x-31.51) + -0.00(x-1.70)(x-4.80)(x-5.98)(x-8.83)(x-12.18)(x-15.21)(x-17.92)(x-19.50)(x-22.23)(x-24.56)(x-27.31)(x-29.11)(x-29.87)(x-30.87)(x-31.51)(x-32.89) + 0.00(x-1.70)(x-4.80)(x-5.98)(x-8.83)(x-12.18)(x-15.21)(x-17.92)(x-19.50)(x-22.23)(x-24.56)(x-27.31)(x-29.11)(x-29.87)(x-30.87)(x-31.51)(x-32.89)(x-33.78) + -0.00(x-1.70)(x-4.80)(x-5.98)(x-8.83)(x-12.18)(x-15.21)(x-17.92)(x-19.50)(x-22.23)(x-24.56)(x-27.31)(x-29.11)(x-29.87)(x-30.87)(x-31.51)(x-32.89)(x-33.78)(x-35.71)