不等距節(jié)點(diǎn)下的牛頓插值公式以及拉格朗日插值公式實(shí)驗(yàn)課報(bào)告

1、數(shù)值分析實(shí)驗(yàn)報(bào)告三插值法（2學(xué)時(shí)）一實(shí)驗(yàn)?zāi)康?.掌握不等距節(jié)點(diǎn)下的牛頓插值公式以及拉格朗日插值公式。二實(shí)驗(yàn)內(nèi)容1.已知函數(shù)表：X93.096.2100.00104.2108.7Y11.3812.8014.7017.0719.91用牛頓插值公式求y （102）的近似值。2.已知函數(shù)表：x1.451.361.14y3.144.155.65用拉格朗日插值公式計(jì)算x = 1.4以及y = 5.01所對(duì)應(yīng)的近似值。三實(shí)驗(yàn)步驟（算法）與結(jié)果1.不等距節(jié)點(diǎn)下的牛頓插值公式I .按差商表計(jì)算n階差商xf f x, x.f Xj, x,+,., x,+n xy0f x0,氣.f Xj, x,+,., x,+n

2、x.f xx .xnynf x , x .f x ,x ，x - f x ,x ，x X =r+4r2rni r+41 in 1i+n iII .按以下公式，帶入X值f (x) = f (x )0+(x x ) f x , x +(x x )(x x ) f x , x , x 01012+.+(x x )(x x )(x x)f x ,x，x 01n 10 1 nIII.得出結(jié)果f (x)程序代碼：#includestdio.h”#includemath.hint main()(int a,i,j;printf(輸入x系數(shù)的個(gè)數(shù)：);scanf(%d”,&a);float d,e=0,c;f

3、loat xa;float ya-1a;printf(輸入x的系數(shù)：);for(i=0;ia;i+)(scanf(%f,&xi);printf(輸入y的系數(shù)：);for(i=0;ia;i+)(scanf(%f,&y0i);for(i=0;ia;i+)(printf(%1.6f ,xi);printf(n);for(i=0；ia;i+)(printf(%1.6f ,y0i);for(j=1；ja;j+)(for(i=0;ia-j;i+)(yji=(yj-1i+1-yj-1i)/(xj+i-xi);printf(n);for(j=1;ja;j+)(for(i=0;ia-j;i+)(printf(%

4、1.6f ,yji);printf(n);printf(”輸入 x 的值：”)；scanf(%f”,&c);for(j=1;ja;j+)(d=1;for(i=0;ij;i+)(d=d*(c-xi);e=e+d*yj0;e=e+y00;printf(%1.6f”,e);return 0;運(yùn)算結(jié)果：15.7936292 .拉格朗日插值公式f (x)= TOC o 1-5 h z (x_氣)(x_氣)(x_x.)f(x)(x -x )(x -x )(x -x )001020 n(x x ) (x x )(x x ) (x x )+0z-1 r+4nf ( x )(x x )(x x )(x x )(

5、x x ) ii 0i i1 ii+1i n+ (x x0)(x 氣)(x % ) f (x )(x x )(x x )(x x ) n n 1 n 20n1+R (x)其中余式R (x) = (x x )(x x ). (x x )f x ,x ,.,x ,x n01n 01 n程序代碼：#includestdio.h#includemath.h int main()(int a,i,j;printf(”輸入x系數(shù)(y的系數(shù))的個(gè)數(shù)：);scanf(%d”,&a);float e,k=1,p=0；float xa;float ya;printf(輸入x的系數(shù)(y的系數(shù))：);for(i=0;ia;i+)(scanf(%f”,&xi);printf(輸入y的系數(shù)(x的系數(shù))：”)；for(i=0;ia;i+)(scanf(%f,&yi);printf(輸入你要求的值：”)；scanf(%f”,&e);for(j=0;ja;j+)(k=1;for(i=0;ia;i+)(if(i=j)(k=k;else(k=k*(e-xi)/(xj-xi);k=k*yj;p=p+k;printf(%f,p);return 0;運(yùn)算結(jié)果:x=1.4 時(shí)，y=3.729525y