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c program of Least Square method for curve fitting.

Implementation of Least-square method for curve fitting.

#include<stdio.h>

#include<conio.h>

#include<math.h>

 main()

{

  float x[10],y[10],a[10][10];

  int i,j,k,n,itr;

  printf("\n ENTER THE SIZE OF MATRIX n:");

  scanf("%d",&n);

  printf("\n ENTER MATRIX ELEMENTS AND RHS:\n");

  for(i=1;i<=n;i++)

  {

    for(j=1;j<=n+1;j++)

    scanf("%f",&a[i][j]);

  }

  for(i=1;i<=n;i++)

  {

    x[i]=0.0;

    y[j]=0.0;

  }

  itr=0.0;

  top:

  itr=itr+1;

  for(i=1;i<=n;i++)

  {

    x[i]=a[i][n+1];

    for(j=1;j<=n;j++)

    {

      if(i==j)

      continue;

     else

     x[i]=x[i]-a[i][j]*x[j];

    }

    x[i]=x[i]/a[i][j];

  }

  for(k=1;k<=n;k++)

  if(fabs(x[k]-y[k])>0.0001)

  {

    printf("\n ITERATION=%d}",itr);

    for(i=1;i<=n;i++)

    {

      y[i]=x[i];

      printf("\n x(%d)=%f",i,x[i]);

    }

    goto top;

    }

    else

    continue;

    return;

    }

c program of simpson's 1/3 rule.

Implementation of Simpson’s 1/3 Rule.

#include<stdio.h>

#include<conio.h>

#include<math.h>

#include<process.h>

#include<string.h>

float fun(float);

void main()

{

  float result=1;

  float a,b;

  float h,sum;

  int i,j;

  int n;

  clrscr();

  printf("\n\n Enter the range-");

  printf("\n\n Lower Limit a-");

  scanf("%f",&a);

  printf("\n\n Lower Limit b-");

  scanf("%f",&b);

  printf("\n\n Enter number of subintervals -");

  scanf("%d",&n);

  h=(b-a)/n;

  sum=0;

  sum=fun(a)+4*fun(a+h)+fun(b);

  for(i=3;i<n;i++)

  {

    sum+=fun(a+(i-1)*h)+4*fun(a+i*h);

  }

  result=sum*h/3;

  printf("\n\n\n\n Value of the integral is %6.4f\t",result);

  printf("\n\n\n Press Enter to Exit");

  getch();

  }

  float fun(float x)

  {

    float temp;

    temp=1/(1+(x*x));

    return temp;

 }

c program of Gauss-seidel method.

Implementation of Gauss-Seidel Method.

#include<stdio.h>

#include<conio.h>

#include<math.h>

 main()

{

  float x[10],y[10],a[10][10];

  int i,j,k,n,itr;

  printf("\n ENTER THE SIZE OF MATRIX n:");

  scanf("%d",&n);

  printf("\n ENTER MATRIX ELEMENTS AND RHS:\n");

  for(i=1;i<=n;i++)

  {

    for(j=1;j<=n+1;j++)

    scanf("%f",&a[i][j]);

  }

  for(i=1;i<=n;i++)

  {

    x[i]=0.0;

    y[j]=0.0;

  }

  itr=0.0;

  top:

  itr=itr+1;

  for(i=1;i<=n;i++)

  {

    x[i]=a[i][n+1];

    for(j=1;j<=n;j++)

    {

      if(i==j)

      continue;

     else

     x[i]=x[i]-a[i][j]*x[j];

    }

    x[i]=x[i]/a[i][j];

  }

  for(k=1;k<=n;k++)

  if(fabs(x[k]-y[k])>0.0001)

  {

    printf("\n ITERATION=%d}",itr);

    for(i=1;i<=n;i++)

    {

      y[i]=x[i];

      printf("\n x(%d)=%f",i,x[i]);

    }

    goto top;

    }

    else

    continue;

    return;

    }

c program of Regular-Falsi Method.

Implementation of Regular-Falsi Method.

#include<stdio.h>

#include<conio.h>

#include<math.h>

#include<string.h>

#include<process.h>

#define EPS 0.00005

#define f(x) 3*x+sin(x)-exp(x)

void FAL_POS();

void main()

{

  clrscr();

printf("\n Solution by FALSE POSITION method\n");

printf("Equation is");

printf("\n\t\t\t 3*x+sin(x)=0\n\n");

FAL_POS();

void FAL_POS()

{

  float f0,f1,f2;

  float x0,x1,x2;

  int i;

printf("Enter the number of iteration:");

scanf("%d",&itr);

for(x1=0.0;;)

{

   f1=f(x1);

if(f1>0)

{

  break;

}

else

{

  x1=x1+0.1;

}

}

x0=x1-0.1;

f0=f(x0);

printf("\n\t\t----------------------------");

printf("\n\t\t     ITERATION\t x2\t\t F(x)\n");

for(i=0;i<itr;i++)

{

  x2=x0-((x1-x0)/(f1-f0))*f0;

  f2=f(x2);

if(f0*f2>0)

{

 x1=x2;

 f1=f2;

}

else

{

x0=x2;

f0=f2;

}

if(fabs(f(2))>EPS)

{

  printf("\n\t\t            %d\t%f\n",i+1,x2,f2);

}

}

printf("\t\t---------------------------");

printf("\n\t\t\tRoot=%f\n",x2);

printf("\t\t---------------------------");

getch();

}

c program of Bisection Method.

Implementation of Bisection Method.

#include<stdio.h>

#include<math.h>

#include<conio.h>

#include<process.h>

#include<string.h>

#define EPS 0.00000005

#define F(x) (x)*log10(x)-1.2

void Bisect();

int count=1,n;

float root=1;

void main()

{

 clrscr();

printf("\n Solution by BISECTION method\n");

printf("\ Equation is");

printf("\n\t\t\t x*log(x)-1.2=0 \n");

printf("\n Enter the number of iterations\n");

scanf("%d",&n);

Bisect();

getch();

}

void Bisect()

{

float x0,x1,x2;

float f0,f1,f2;

for(x2=1; ;x2++)

{

f2=F(x2);

if(f2>0)

{

break;

}

}

for(x1=x2-1; ;x2++)

{

f1=F(x1);

if(f1<0)

{

break;

}

}

printf("\t\t----------------------------------------");

printf("\n\t\t ITERATIONS\t\t\  ROOTS\n");

printf("\t\t-----------------------------------------");

for(;count<n;count++)

{

x0=(x1+x2)/2.0;

f0=F(x0);

if(f0==0)

{

root=x0;

}

if(f0*f1<0)

{

x2=x0;

}

else

{

x1=x0;

f1=f0;

}

printf("\n\t\t ITERATION%d",count);

printf("\t  :\t   %f",x0);

if(fabs((x1-x2)/x1) <EPS)

{

printf("\n\t\t--------------------------------");

printf("\n\t\t       Root= %f",x0);

printf("\n\t\t   Iterations = %d\n",count);

printf("\t\t-----------------------------------");

getch();

exit(0);

}

}

printf("\n\t\t-------------------------------------");

printf("\n\t\t\t Root = %7.4f",x0);

printf("\n\t\t\t  Iteration = %d\n", count-1);

printf("\t\t---------------------------------------");

getch();}

c program of Trapezoidal Rule.

Implementation of Trapezoidal Rule.

#include<stdio.h>

#include<conio.h>

#include<string.h>

#include<math.h>

#include<process.h>

float fun(float);

void main()

{

 float result=1;

 float a,b;

 float h,sum;

 int i,j;

 int n;

 clrscr();

 printf("\n\n Enter the range-");

 printf("\n\n Lower Limit a-");

 scanf("%f",&a);

 printf("\n\n Upper Limit b-");

 scanf("%f",&b);

 printf("\n\n Enter number of subintervals-");

 scanf("%d",&n);

 h=(b-a)/n;

 sum=0;

 sum=fun(a)+fun(b);

 for(i=1;i<n;i++)

 {

   if(i%3==0)

   {

     sum+=2*fun(a+i*h);

     }

    

       result=sum*h/2;

       printf("\n\n\n Value of the intergal is %6.4f\t",result);

       printf("Press enter to Exit");

       getch();

       }

       float fun(float x)

       {

           float temp;

         temp=1/(1+(x*x));

         return temp;

        }  

c program of simpson's 3/8 rule.

C  Propgram to implement simpson's 3/8rd rule.

#include<stdio.h>

#include<math.h>

#include<conio.h>

#include<process.h>

#include<string.h>

float fun(float);

void main()

{

 float result=1;

 float a,b;

 float h,sum;

 int i,j;

 int n;

 clrscr();

 printf("\n\n Enter the range-");

 printf("\n\n Lower Limit a-");

 scanf("%f",&a);

 printf("\n\n Upper Limit b-");

 scanf("%f",&b);

 printf("\n\n Enter number of subintervals-");

 scanf("%d",&n);

 h=(b-a)/n;

 sum=0;

 sum=fun(a)+fun(b);

 for(i=1;i<n;i++)

 {

   if(i%3==0)

   {

     sum+=2*fun(a+i*h);

     }

     else

     {

       sum+=3*fun(a+(i)*h);

       }

       }

       result=sum*3*h/8;

       printf("\n\n\n Value of the intergal is %6.4f\t",result);

       printf("Press enter to Exit");

       getch();

       }

       float fun(float x)

       {

             float temp;

             temp=1/(1+(x*x));

             return temp;

             }

c programe of Newton backward interpolation formula

Implementatio of Newton’s Backward Interpolation Formula.

#include<stdio.h>

#include<conio.h>

#include<math.h>

#include<process.h>

#include<string.h>

void main()

{

  int n;

  int i,j,k;

  float mx[10];

  float my[10];

  float x;

  float x0=0;

  float y0;

  float sum;

  float h;

  float fun;

  float p;

  float diff[20][20];

  float y1,y2,y3,y4;

  clrscr();

  printf("\n Enter the number of term -");

  scanf("%d",&n);

  printf("\n Enter the value in the form of x - -");

  for(i=0;i<n;i++)

  {

     printf("\n Enter the value of x%d  -",i+1);

     scanf("%f",&mx[i]);

  }

  printf("\n Enter the value in the form of y - -");

  for(i=0;i<n;i++)

  {

     printf("\n Enter the value of y%d  -",i+1);

     scanf("%f",&my[i]);

  }

   printf("\n Enter the value of x for- -");

   printf("\n which you want the value of y -");

   scanf("%f",&x);

   h=mx[1]-mx[0];

   for(i=0;i<n-1;i++)

   {

     diff[i][1]=my[i+1]-my[i];

   }

   for(j=2;j<=4;j++)

   {

     for(i=0;i<n-j;i++)

     {

               diff[i][j]=diff[i+1][j-1]-diff[i][j-1];

     }

  }

  i=0;

  while(!mx[i]>x)

  {

   i++;

   }

   x0=mx[i];

   sum=0;

   y0=my[i];

   fun=1;

   p=(x-x0)/h;

   sum=y0;

   for(k=1;k<=4;k++)

   {

     fun=(fun*(p-(k-1)))/k;

     sum=sum+fun*diff[i][k];

   }

   printf("\n when x=%6.4f,y=%6.8f",x,sum);

   printf("\n\n\n Press Enter to Exit");

   getch();

   }