C++-數(shù)值分析列主元高斯消去法-列主元LU分解法-Jacobi迭

1、 temp=temp+Aij*Yj;Yi=Bi-temp;/求解UX=YXN-1=YN1/AN1N1;for(i=N-2;i=0;i)doubletemp=0;for(intj=i+1;jN;j+)temp=temp+Aij*Xj;Xi=(Yitemp)/Aii;/打印Xcout線性方程組的解(XI,X2,X3Xn)為:endl;for(i=0;iN;i+)coutXi;運(yùn)行結(jié)果截圖：0-1001kl2-1BB0-12-1100-126關(guān)性方程組的解(Hi,X2,X3Xn)申；1.21.41.6Q.8PressQnykeytocontinue7簡單迭代法（Jacobi迭代）:測試矩陣為：=取精

2、度為esp=0.001,最大迭代次數(shù)M=100源代碼：Jacobi.cpp#include#include#defineN4/矩陣的維數(shù)，可按需更改staticdoubleANN=2,-1,0,0,-1,2,-1,0,0,-1,2,-1,0,0,-1,2;/系數(shù)矩陣staticdoubleBN=1,0,1,0;/右端項(xiàng)staticdoubleYN;/輸出比較項(xiàng)staticdoubleYN;staticdoubleXN;/輸出項(xiàng)staticdoubleGN;/X=BX+G的G矩陣inti,j,k;/計(jì)數(shù)器doubleeps=0.001;intM=100;booldistance()/求兩輸出項(xiàng)的

3、差的范數(shù)是否滿足精度要求doubletemp=0;for(i=0;ieps)returnfalse;elsereturntrue;/滿足精度要求則結(jié)束程序voidmain()/形成迭代矩陣B，存放到A中for(i=0;iN;i+)if(fabs(Aii)eps)cout打印失敗endl;return;doubleT=Aii;for(j=0;jN;j+)Aij=-Aij/T;Aii=0;Gi=Bi/T;intcounter=0;while(counterM)/迭代for(i=0;iN;i+)doubletemp=0;for(j=O;jN;j+)temp=temp+Aij*Yj;Xi=Gi+tem

4、p;if(distance()=true)break;else/交換X,Y向量；for(i=0;iN;i+)Yi=Xi;counter+;/打印Xcout迭代次數(shù)為：counter次。該線性方程組的解(XI,X2,X3Xn)為：endl;for(i=0;iN;i+)coutXi;運(yùn)行結(jié)果截圖：迭憂次數(shù)為：陽灰，該線性方程組的解壯，就，題而為:1.199221.398981.598740.799371Pressanyke/tocontinue8Seidel迭代:測試矩陣為：=取精度為esp=0.001,最大迭代次數(shù)M=100源代碼：Seidel.cpp#includeiostream.h#inc

5、lude#defineN4/矩陣的維數(shù)，可按需更改staticdoubleANN=2,-1,0,0,-1,2,-1,0,0,-1,2,-1,0,0,-1,2;/系數(shù)矩陣staticdoubleBN=1,0,1,0;/右端項(xiàng)staticdoubleYN;/輸出比較項(xiàng)staticdoubleXN;/輸出項(xiàng)staticdoubleGN;/X=BX+G的G矩陣inti,j,k;/計(jì)數(shù)器doubleeps=0.001;intM=100;booldistance()/求兩輸出項(xiàng)的差的范數(shù)是否滿足精度要求doubletemp=0;for(i=0;ieps)returnfalse;elsereturntrue

6、;/滿足精度要求則結(jié)束程序voidmain()/形成迭代矩陣B,存放到A中for(i=0;iN;i+)if(fabs(Aii)eps)cout打印失敗endl;return;doubleT=Aii;for(j=0;jN;j+)Aij=-Aij/T;Aii=0;Gi=Bi/T;intcounter=0;while(counterM)/迭代for(i=0;iN;i+)doubletemp=0;for(j=O;jN;j+)temp=temp+Aij*Xj;Xi=Gi+temp;if(distance()=true)break;else/交換X,Y向量；for(i=0;iN;i+)Yi=Xi;coun

7、ter+;cout迭代次數(shù)為：counter次。該線性方程組的解(XI,X2,X3Xn)為：endl;for(i=0;iN;i+)coutXi;9松弛法（SOR迭代）測試矩陣為：取松弛系數(shù)w=1.46=取精度為esp=0.001,最大迭代次數(shù)M=100源代碼：SOR.cpp#includeiostream.h#includemath.h#defineN4/矩陣的維數(shù)，可按需更改staticdoubleANN=2,-1,0,0,-1,2,-1,0,0,-1,2,-1,0,0,-1,2;/系數(shù)矩陣staticdoubleBN=1,0,1,0;/右端項(xiàng)staticdoubleYN;/輸出比較項(xiàng)sta

8、ticdoubleXN;/輸出項(xiàng)staticdoubleGN;/X=BX+G的G矩陣inti,j,k;/計(jì)數(shù)器doubleeps=0.001;/最小容許誤差intM=100;/最大容許比較次數(shù)doublew=1.46;/松弛因子booldistance()/求兩輸出項(xiàng)的差的范數(shù)是否滿足精度要求doubletemp=0;for(i=0;ieps)returnfalse;elsereturntrue;/滿足精度要求則結(jié)束程序voidmain()/形成迭代矩陣B,存放到A中for(i=0;iN;i+)if(fabs(Aii)eps)cout打印失敗endl;return;doubleT=Aii;for(j=0;jN;j+)Aij=-w*Aij/T;Aii=1-w;Gi=w*Bi/T;intcounter=0;while(counterM)/迭代for(i=0;iN;i+)doubletemp=0;for(j=0;jN;j+)temp=temp+Aij*Xj;Xi=Gi+temp;if(distance()=true)break;else/交換X,Y向量；for(i=0;iN;i+)Yi=Xi;counter+;cout迭代次數(shù)為：cou