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NM_10

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  1. #include<stdio.h>
  2. #include<conio.h>
  3. #include<math.h>
  4.  
  5. #define f1(x,y,z)  (17-y+2*z)/20
  6. #define f2(x,y,z)  (-18-3*x+z)/20
  7. #define f3(x,y,z)  (25-2*x+3*y)/20
  8. #define EPS 0.001
  9.  
  10. int main()
  11. {
  12.     float x0=0, y0=0, z0=0, x1, y1, z1, e1, e2, e3, e;
  13.     int count=1;
  14.     printf("\nCount\tx\ty\tz\n");
  15.     do
  16.         {
  17.             /* Calculation */
  18.             x1 = f1(x0,y0,z0);
  19.             y1 = f2(x0,y0,z0);
  20.             z1 = f3(x0,y0,z0);
  21.             printf("%d\t%0.4f\t%0.4f\t%0.4f\n",count, x1,y1,z1);
  22.  
  23.             /* Error */
  24.             e1 = fabs(x0-x1);
  25.             e2 = fabs(y0-y1);
  26.             e3 = fabs(z0-z1);
  27.  
  28.             count++;
  29.  
  30.             /* Set value for next iteration */
  31.               x0 = x1;
  32.               y0 = y1;
  33.               z0 = z1;
  34.         }while(e1>e && e2>e && e3>e);
  35.        
  36.         printf("\nSolution: x=%0.3f, y=%0.3f and z = %0.3f\n",x1,y1,z1);
  37.        
  38.     getch();
  39.     return 0;
  40. }
  41.  
  42.  
  43.  
  44. #include<stdio.h>
  45. #include<conio.h>
  46. #include<math.h>
  47.  
  48. /* Arrange systems of linear
  49.    equations to be solved in
  50.    diagonally dominant form
  51.    and form equation for each
  52.    unknown and define here
  53. */
  54. /* In this example we are solving
  55.    3x + 20y - z = -18
  56.    2x - 3y + 20z = 25
  57.    20x + y - 2z = 17
  58. */
  59. /* Arranging given system of linear
  60.    equations in diagonally dominant
  61.    form:
  62.    20x + y - 2z = 17
  63.    3x + 20y -z = -18
  64.    2x - 3y + 20z = 25
  65. */
  66. /* Equations:
  67.    x = (17-y+2z)/20
  68.    y = (-18-3x+z)/20
  69.    z = (25-2x+3y)/20
  70. */
  71. /* Defining function */
  72. #define f1(x,y,z)  (17-y+2*z)/20
  73. #define f2(x,y,z)  (-18-3*x+z)/20
  74. #define f3(x,y,z)  (25-2*x+3*y)/20
  75. #define e 0.001
  76. /* Main function */
  77. int main()
  78. {
  79.  float x0=0, y0=0, z0=0, x1, y1, z1, e1, e2, e3;
  80.  int count=1;
  81.  
  82.  printf("\nCount\tx\ty\tz\n");
  83.  do
  84.  {
  85.   /* Calculation */
  86.   x1 = f1(x0,y0,z0);
  87.   y1 = f2(x1,y0,z0);
  88.   z1 = f3(x1,y1,z0);
  89.   printf("%d\t%0.4f\t%0.4f\t%0.4f\n",count, x1,y1,z1);
  90.  
  91.   /* Error */
  92.   e1 = fabs(x0-x1);
  93.   e2 = fabs(y0-y1);
  94.   e3 = fabs(z0-z1);
  95.  
  96.   count++;
  97.  
  98.   /* Set value for next iteration */
  99.   x0 = x1;
  100.   y0 = y1;
  101.   z0 = z1;
  102.  
  103.  }while(e1>e && e2>e && e3>e);
  104.  
  105.  printf("\nSolution: x=%0.3f, y=%0.3f and z = %0.3f\n",x1,y1,z1);
  106.  
  107.  getch();
  108.  return 0;
  109. }
  110.  
  111.  
  112.  
  113. #include<stdio.h>
  114. #include<conio.h>
  115. #include<math.h>
  116. #define MAXIT 10
  117. #define EPS 0.001
  118. int main()
  119. {
  120.     int i,j,n,A[20][20],X[20][2],count=1;
  121.     float Xo[20][2],Xn[20][2],Xmax=0;
  122.     printf("Enter the size of the matrix A : ");scanf("%d",&n);
  123.     printf("\nEnter the elements of the %d*%d matrix A\n",n,n);
  124.     for(i=1;i<=n;i++)
  125.     {for(j=1;j<=n;j++)
  126.         {printf("\nA[%d][%d] : ",n,n);scanf("%d",&A[i][j]);}
  127.     }
  128.    
  129.     printf("\nEnter the initial Guess Vector X : \n");
  130.     for(i=1;i<=n;i++)
  131.     {
  132.         printf("Enter X[%d][1] : ",i);scanf("%d",&X[i][1]);
  133.     }
  134.    
  135.     Xo[1][1]=A[1][1]*X[1][1]+A[1][2]*X[2][1]+A[1][3]*X[3][1];
  136.     Xo[2][1]=A[2][1]*X[1][1]+A[2][2]*X[2][1]+A[2][3]*X[3][1];
  137.     Xo[3][1]=A[3][1]*X[1][1]+A[3][2]*X[2][1]+A[3][3]*X[3][1];
  138.    
  139.     for(i=1;i<=n;i++)
  140.     {
  141.         if(Xo[i][1]>Xmax)
  142.         {Xmax = Xo[i][1];}
  143.     }
  144.    
  145.     Xn[1][1] = Xo[1][1]/Xmax;
  146.     Xn[2][1] = Xo[2][1]/Xmax;
  147.     Xn[3][1] = Xo[3][1]/Xmax;
  148.     count++;
  149.     if((fabs(Xn[1][1]-Xo[1][1])<EPS)&&(fabs(Xn[1][1]-Xo[1][1])<EPS)&&(fabs(Xn[1][1]-Xo[1][1])<EPS)||count<MAXIT)
  150.     printf("\nThe Required Eigen Value is : %f",Xmax);
  151.     printf("\nThe Required Eigen Vector is :\n");
  152.     printf("\n|%.3f|",Xn[1][1]);
  153.     printf("\n|%.3f|",Xn[2][1]);
  154.     printf("\n|%.3f|",Xn[3][1]);
  155.     getch();
  156.     return 0;
  157. }
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