解線性方程組.doc

#include#include#define n 3/2-1順序解線性方程組void Cgauss(float ann,float bn,float xn)int i,j,k;float sum=0.0;for(k=0;kn;k+)for(j=k+1;jn;j+)/歸一化 if(akk)akj/=akk; / printf(a%d%d=%fn ,k,j,akj);bk/=akk;akk=1;for(i=k+1;in;i+)/消元for(j=k+1;j=0;i-)sum=0.0;for(j=n-1;ji;j-)sum=sum+aij*xj;xi=bi-sum;/2-2順序解線性方程組void Cgauss1(float ann,float bn,float xn)int i,j,k;float temp,sum=0.0;for(k=0;kn;k+)for(i=k+1;ifabs(akk)&akk!=0)for(j=k;jn;j+)temp=akj;akj=aij;aij=temp;temp=bk;bk=bi;bi=temp;for(j=k+1;jn;j+)/歸一化 akj=akj/akk; bk=bk/akk;akk=1;for(i=k+1;in;i+)for(j=k+1;j=0;i-)sum=0.0;for(j=n-1;ji;j-)sum=sum+aij*xj;xi=bi-sum;/2-3順序解線性方程組void Cgauss2(float ann,float bn,float xn)int i,j,is,jsn,k;float temp,max,t,sum=0.0;for(k=0;kn-1;k+)max=0.0;for(i=k;in;i+)for(j=k;j max)max=t,jsk=j,is=i; if(max+1.0=1.0) printf(矩陣異常!);elseif(jsk!=k)/列交換,每次列交換都是全部交換，因此i是從0開(kāi)始for(i=0;in;i+) temp=aik,aik=aijsk,aijsk=temp;if(is!=k)/行交換for(j=k;jn;j+) temp=akj,akj=aisj,aisj=temp; temp=bk,bk=bis,bis=temp;for(j=k+1;jn;j+)/歸一化 akj=akj/akk;bk=bk/akk;akk=1;for(i=k+1;in;i+)/消元for(j=k+1;j=0;i-)sum=0.0;for(j=n-1;ji;j-)sum=sum+aij*xj;xi=bi-sum;void main()int i,j;float ann=1,2,-2,2,1,2,3,0,4, bn=2,3,1,xn;printf(方程各元素如下:n);for(i=0;in;i+)for(j=0;jn;j+)printf(%.2f ,aij);printf(n);printf(方程常數(shù)依次為:n);for(i=0;in;i+)printf(%.2f ,bi);printf(n); printf(-順序解線性方程組-n);Cgauss(a,b,x);printf(-列選元解線性方程組-n);Cgauss1(a,b,x);printf(-全選組元解線性方程組-n);Cgauss2(a,b,x);printf(方程解為:n);for(i=0;in;i+)printf(x%d=%.2f ,i,xi);printf(n); /2-4 Crout分解法解線性方程組#include#include#include#define n 3void Crout(float ann,float bn,float xn)int r,i,k;float Lnn, Unn,yn,sum;for(i=0;in;i+) /L的第一列Li0=ai0;for(i=0;in;i+) /U的第一行U0i=a0i/L00;Uii=1;for(r=1;rn-1;r+)for(i=r+1;in;i+)sum=0.0;for(k=0;kr;k+)sum+=Lrk*Uki;Uri=(ari-sum)/Lrr;for(r=1;rn;r+)for(i=r;in;i+)sum=0.0;for(k=0;kr;k+)sum+=Lik*Ukr;Lir=air-sum;y0=b0/L00;for(r=1;rn;r+)sum=0.0;for(i=0;ir;i+)sum+=Lri*yi;yr=(br-sum)/Lrr;for(i=0;i=0;r-)sum=0.0;for(i=r+1;in;i+)sum+=Uri*xi;xr=yr-sum;void main()int i,j;float ann=1,-1,3,2,-4,6,4,-9,2, bn=1,4,1,xn;printf(方程各元素如下:n);for(i=0;in;i+)for(j=0;jn;j+)printf(%.2f ,aij);printf(n);printf(方程常數(shù)依次為:n);for(i=0;in;i+)printf(%.2f ,bi);printf(n);Crout(a,b,x);/*printf(需解線性方程組消元后為:n);for(i=0;in;i+)for(j=0;jn;j+)printf(%.2f ,aij);printf(n);printf(方程常數(shù)消元后為:n);for(i=0;in;i+)printf(%.2f ,bi);printf(n);*/printf(方程解為:n);for(i=0;in;i+)printf(x%d=%.2f ,i,xi);printf(n);/2-5 Doolittle分解法解線性方程組#include#include#include#define n 3void Doolittle(float ann,float bn,float xn)int r,i,k,j;float Lnn=0, Unn=0,yn=0,sum; /*初始化矩陣l*/ for(i=0; in; i+) for(j=0; jn; j+) if(i=j) Lij = 1; /*開(kāi)始LU分解*/ /*第一步：對(duì)矩陣U的首行進(jìn)行計(jì)算*/ for(i=0; in; i+) U0i = (float)(a0i/L00); /*第二步：逐步進(jìn)行LU分解*/ for(i=0; in-1; i+) /*對(duì)“L列”進(jìn)行計(jì)算*/ for(j=i+1; jn; j+) for(k=0,sum=0; kn; k+) if(k != i) sum += Ljk*Uki; Lji = (float)(aji-sum)/Uii); /*對(duì)“U行”進(jìn)行計(jì)算*/ for(j=i+1; jn; j+) for(k=0,sum=0; kn; k+) if(k != i+1) sum += Li+1k*Ukj; Ui+1j = (float)(ai+1j-sum); printf(矩陣L：n); for(i=0; in; i+) for(j=0; jn; j+) printf(%0.3f , Lij); printf(n); / 輸出矩陣u printf(矩陣U：n); for(i=0; in; i+) for(j=0; jn; j+) printf(%0.3f , Uij); printf(n); y0=b0;for(r=1;rn;r+)sum=0.0;for(i=0;ir;i+)sum+=Lri*yi;yr=br-sum; printf(解得y為：n); for(i=0;i=0;r-)sum=0.0;for(i=r+1;in;i+)sum+=Uri*xi;xr=(yr-sum)/Urr;printf(方程解為:n);for(i=0;in;i+)printf(x%d=%.4f ,i,xi);printf(n);void main()int i,j; float xn; /定義數(shù)組Xfloat ann=1,-1,3,2,-4,6,4,-9,2, bn=1,4,1;printf(-Doolittle分解法解線性方程組-n);printf(方程各元素如下:n);for(i=0;in;i+)for(j=0;jn;j+)printf(%.4f ,aij);printf(n);printf(方程常數(shù)依次為:n);for(i=0;in;i+)printf(%.4f ,bi);printf(n);Doolittle(a,b,x);2-6 平方根法解線性方程組#include#include#include#define n 3void Ssqrt(float ann,float bn,float xn)int j,i,k;float Lnn=0,yn,sum;/L00=(float)sqrt(a00);for(j=0;jn;j+)for(i=j;in;i+)if(i=j)sum=0.0;for(k=0;kj;k+)sum+=Ljk*Ljk;Ljj=(float)sqrt(ajj-sum);elsesum=0.0;for(k=0;kj;k+)sum+=Lik*Ljk;Lij=(aij-sum)/Ljj; printf(矩陣L：n); for(i=0; in; i+) for(j=0; jn; j+) printf(%0.3f , Lij); printf(n); y0=b0/L00;for(i=1;in;i+)sum=0.0;for(k=0;ki;k+)sum+=Lik*yk;yi=(bi-sum)/Lii;printf(解得y為:n);for(i=0;i=0;i-)sum=0.0;for(k=i+1;kn;k+)sum+=Lki*xk;xi=(yi-sum)/Lii;printf(方程解x為:n);for(i=0;in;i+)printf(x%d=%.4f ,i,xi);printf(n);void main()int i,j;float ann=4,-1,1,-1,4.25,2.75,1,2.75,3.5, bn=0,1,0,xn;printf(-平方根法解線性方程組-n);printf(方程各元素如下:n);for(i=0;in;i+)for(j=0;jn;j+)printf(%.4f ,aij);printf(n);printf(方程常數(shù)依次為:n);for(i=0;in;i+)printf(%.4f ,bi);printf(n);Ssqrt(a,b,x);2-7追趕法解線性方程組#include#include#include#define n 4void Chase(float Ann,float fn,float xn)int i,j;float an, bn,cn,a1n, b1n,c1n,yn;/系數(shù)矩陣用三個(gè)一維數(shù)組表示for(i=1,j=0;in,jn-1;i+,j+)ai=Aij;for(i=0;in;i+)bi=Aii;for(i=0,j=1;in-1,jn;i+,j+)ci=Aij;/for(i=1;in;i+)a1i=ai;b10=b0;for(j=0,i=1;jn-1,in;j+,i+)c1j=cj/b1j;b1i=bi-a1i*c1i-1;y0=f0/b10;for(i=1;in;i+)yi=(fi-a1i*yi-1)/b1i;printf(解得y為:n);for(i=0;i=0;i-)xi=yi-c1i*xi+1;printf(方程解為:n);for(i=0;in;i+)printf(x%d=%.4f ,i,xi);pri