added

DJacobiEigen01.c

@@ -0,0 +1,143 @@
+//  
+//  Jacobi eigenvalue algorithm:
+//  ============================
+//  
+//  Jacobi eigenvalue algorithm is an iterative method for calculation of the
+//  eigenvalues and eigenvectors of a symmetric matrix.
+//  This program finds all the eigenvalues and the corresponding eigenvectors
+//  of a real symmetric matrix. 
+//  Assume that the given matrix is real symmetric.
+//
+#include <stdio.h>
+#include <math.h>
+
+void main() {
+  int n, i, j, p, q, flag;
+  double a[10][10], d[10][10], s[10][10], s1[10][10], s1t[10][10];
+  double temp[10][10], theta, zero=1e-5, max, pi=3.141592654;
+
+  printf("Enter the size of the matrix ");
+  scanf("%d",&n);
+
+  printf("Enter the elements row wise \n");
+  for(i=0; i<n; i++) {
+    for(j=0; j<n; j++)  scanf ("%lf", &a[i][j]);
+  }
+
+  printf("The given matrix is\n");
+  for(i=0; i<n; i++) {
+    for(j=0; j<n; j++)  printf ("%8.4f ", a[i][j]);
+    printf ("\n");
+  }
+  printf ("\n");
+
+  for(i=0; i<n; i++) {
+    for(j=0; j<n; j++) {
+      d[i][j]= a[i][j];
+      if(i==j)
+        s[i][j]= 1;
+      else
+        s[i][j]= 0;
+    }
+  }
+
+  do {
+    flag= 0;
+    p=0; q=1;
+    max= fabs(d[p][q]);
+
+    for(i=0; i<n; i++) {
+      for(j=0; j<n; j++) {
+        if(i!=j) {
+          if (max < fabs(d[i][j])) {
+            max= fabs(d[i][j]);
+            p= i;
+            q= j;
+          }
+        }
+      }
+    }
+
+    if(d[p][p]==d[q][q]) {
+      if (d[p][q] > 0)
+        theta= pi/4;
+      else
+        theta= -pi/4;
+    }
+    else {
+      theta=0.5*atan(2*d[p][q]/(d[p][p]-d[q][q]));
+    }
+
+    for(i=0; i<n; i++) {
+      for(j=0; j<n; j++) {
+        if(i==j) {
+         s1[i][j]= 1;
+         s1t[i][j]= 1;
+        }
+        else {
+          s1[i][j]= 0;
+          s1t[i][j]= 0;
+        }
+      }
+    }
+
+    s1[p][p]= cos(theta);
+    s1t[p][p]= s1[p][p];
+
+    s1[q][q]= cos(theta);
+    s1t[q][q]= s1[q][q];
+
+    s1[p][q]= -sin(theta);
+    s1[q][p]= sin(theta);
+
+    s1t[p][q]= s1[q][p];
+    s1t[q][p]= s1[p][q];
+
+    for(i=0; i<n; i++) {
+      for(j=0; j<n; j++) {
+        temp[i][j]= 0;
+        for(p=0; p<n; p++)  temp[i][j]+= s1t[i][p]*d[p][j];
+      }
+    }
+
+    for(i=0; i<n; i++) {
+      for(j=0; j<n; j++) {
+        d[i][j]= 0;
+        for(p=0; p<n; p++)  d[i][j]+= temp[i][p]*s1[p][j];
+      }
+    }
+
+    for(i=0; i<n; i++) {
+      for(j=0; j<n; j++) {
+        temp[i][j]= 0;
+        for(p=0; p<n; p++)  temp[i][j]+= s[i][p]*s1[p][j];
+      }
+    }
+
+    for(i=0; i<n; i++) {
+      for(j=0; j<n; j++)  s[i][j]= temp[i][j];
+    }
+
+    for(i=0; i<n; i++) {
+      for(j=0; j<n; j++) {
+        if(i!=j)
+          if(fabs(d[i][j]) > zero) flag= 1;
+      }
+    }
+  } while(flag==1);
+
+  printf("The eigenvalues are \n");
+  for(i=0; i<n; i++)
+    printf("%8.4lf ",d[i][i]);
+  printf("\nThe corresponding eigenvectors are \n");
+
+  for(j=0; j<n; j++) {
+    printf("(");
+    for(i=0; i<n-1; i++)
+      printf("% 8.4lf,",s[i][j]);
+    printf("%8.4lf )^T\n",s[n-1][j]);
+  }
+}
+
+
+

DemoAssignment1.c

@@ -0,0 +1,120 @@
+#include<stdio.h>
+#include<stdlib.h>
+
+int main()
+{
+	double x[4]={0,1,2,3},b[4][1]={1,0,1,2};
+	double a[4][3],at[3][4],A[3][3],B[3][1],mat[3][4]; 
+
+	for(int i=0;i<4;i++)
+	{
+		a[i][0]=1;
+		a[i][1]=x[i];
+		a[i][2]=x[i]*x[i];
+		//a[i][3]=x[i]*x[i]*x[i];
+	}
+
+
+	/** making transpose matrix **/ 
+	for(int i=0;i<3;i++) 
+	{
+		for(int j=0;j<4;j++) 
+		{
+			at[i][j]=a[j][i]; 
+		} 
+	} 
+
+
+	/* multilication of transpose matrix X matrix */
+	for(int i=0;i<3;i++) 
+	{
+		for(int j=0;j<4;j++) 
+		{
+			A[i][j]=0;
+		} 
+	} 
+
+	for(int i=0;i<3;i++) 
+	{
+		for(int j=0;j<3;j++) 
+		{
+			for(int k=0;k<4;k++)
+			{
+				A[i][j]+=(at[i][k]*a[k][j]); 
+			}
+		} 
+	} 
+
+
+	/* updating B */
+	for(int i=0;i<3;i++) 
+	{
+		for(int j=0;j<1;j++) 
+		{
+			B[i][j]=0;
+		} 
+	} 
+
+	for(int i=0;i<3;i++) 
+	{
+		for(int j=0;j<1;j++) 
+		{
+			for(int k=0;k<4;k++)
+			{
+				B[i][j]+=(at[i][k]*b[k][j]); 
+			}
+		} 
+	} 
+
+
+	/** using gauss elimination process to find the least square fitted values **/
+	for(int i=0;i<3;i++)
+	{
+		for(int j=0;j<3;j++) 
+		{
+			mat[i][j]=A[i][j];
+		} 
+		mat[i][3]=B[i][0];
+	}
+
+
+	/** upper triangular matrix **/
+	for(int j=0;j<3;j++)
+	{
+		for(int i=j+1;i<3;i++) 
+		{
+			int m=mat[j][j];
+			int n=mat[i][j]; 
+
+			for(int k=0;k<=3;k++) 
+			{
+				mat[i][k]=(m*mat[i][k])-(n*mat[j][k]);
+			} 
+		} 
+	}
+
+
+	/** back substitution **/ 
+	double ans[3];
+	ans[3-1]=(mat[3-1][3]/mat[3-1][3-1]);
+
+	for(int j=3-2;j>-1;j--)
+	{
+		double sum=0;
+		for(int i=j+1;i<3;i++) 
+		{
+			sum+=(mat[j][i]*ans[i]); 
+			//printf("sum %9.3lf\n",sum);
+		} 
+
+		ans[j]=(mat[j][3]-sum)/(mat[j][j]);
+	}
+
+
+	/** answer **/
+	for(int i=0;i<3;i++) 
+	{
+		printf("c%d = %9.3lf\n",i+1,ans[i]);
+	}
+}
+

falsepositionmethod.c

@@ -0,0 +1,51 @@
+#include<stdio.h>
+#include<stdlib.h>
+#include<math.h>
+#define MAXN 200
+#define F(X) ((X*X*X) + (4*X*X)-10)
+
+int main()
+{
+	double a,b,p,tol,fa,fb,fp;
+	a=1.25,b=1.5,tol=10.e-6;
+	int i=0;
+	fa=F(a),fb=F(b); 
+
+	if(fa*fb>=0) 
+	{
+		puts("no root");
+		return EXIT_FAILURE; 
+	}
+
+	puts("a	      b        c         f(a)         f(b)          f(c)");	
+
+	while(i<MAXN)
+	{
+
+		i++;
+		p=((a*fb)-(b*fa))/(fb-fa);
+		fp=F(p);
+		printf("%lf\t%lf\t%lf\t%lf\t%lf\t%lf\n",a,b,p,fa,fb,fp);
+		if(fabs(fp)<=tol) 
+		{
+			printf("the approaximate solution is = %lf\n",p); 
+			printf("iteration number =%d\n",i);
+			return EXIT_SUCCESS;
+		}  
+		else 
+		{
+			if(fp*fa<0) 
+			{
+				b=p;
+				fb=fp; 
+			} 
+			else 
+			{
+				a=p;
+				fa=fp; 
+			}
+		} 
+
+	}
+	printf("iteration overflow . . . "); 
+}