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Author: Hrithik Raj

Gauss-Elimination.cpp

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+/* Gauss elimination method */
+#include <iostream>
+#include <iomanip>
+#include <math.h>
+#define N 4
+using namespace std;
+int main(){
+    float a[N][N+1],x[N],t,s;
+    int i,j,k;
+    cout << "Enter the elements of the"
+            "augmented matrix rowwise" << endl;
+    cout << fixed;
+    for (i=0;i<N;i++)
+        for (j=0;j<N+1;j++)
+            cin >> a[i][j]);
+    for (j=0;j<N-1;j++)
+        for (i=j+1;i<N;i++){
+            t = a[i][j]/a[j][j];
+                for (k=0;k<N+1;k++)
+                    a[i][k] -= a[j][k]*t;
+        }
+    /* now printing the
+    upper triangular matrix */
+    cout << "The upper triangular matrix"
+            "is:-" << endl;
+    for (i=0;i<N;i++){
+        for (j=0;j<N+1;j++)
+            cout << setw(8) << setprecision(4) << a[i][j];
+            cout << endl;
+    }
+    /* now performing back substitution */
+    for (i=N-1;i>=0;i--){
+    s = 0;
+        for (j=i+1;j<N;j++)
+            s += a[i][j]*x[j];
+            x[i] = (a[i][N]-s)/a[i][i];
+    }
+    /* now printing the results */
+    cout << "The solution is:- " << endl;
+    for (i=0;i<N;i++)
+        cout << "x[" << setw(3) << i+1 << "] = "
+        << setw(7) << setprecision(4) << x[i] << endl;
+    return 0;
+}