spline

void computeCubicSplineCoefficients(double** a, double* x, double* y, int n)
{
	double** matrix = new double*[n-1];
	for (int i=0; i<n-1; i++)
		matrix[i] = new double[n-1];
	double* sol = new double[n-1];
	double* rhs = new double[n-1];

	/* Füllen Sie hier die Matrix und die rechte Seite mit den entsprechenden Werten. */
	for(int i=0;i<n-1;++i)
	{	
		double h1 = x[i+1]-x[i];
		double h2 = x[i+2]-x[i+1];

		if(i-1>=0)
			matrix[i][i-1]=h1;
		matrix[i][i]= 2*(h1+h2);
		if(i+1<n-1)
			matrix[i][i+1]=h2;


		rhs[i] = 3*((y[i+2]-y[i+1])/h2-(y[i+1]-y[i])/h1);
	}

	// solve
	solveByGaussSeidel(sol, matrix, rhs, n-1);
	for(int i=1;i<n;++i)
	{
		a[i][2]=sol[i-1];
	}
	for(int i=1;i<n;++i)
	{
		double hi = x[i] - x[i-1];
		a[i][0] = y[i];
		a[i][1] = ((y[i]-y[i-1])/hi)+hi/3.0*(2*a[i][2]+a[i-1][2]);
		a[i][3] = (a[i-1][2]-a[i][2])/(3*hi);		
	}

	/* Berechnen Sie hier die Koeffizienten a unter Verwendung der Lösung des LGS. */
	for(int i=0;i<n;++i)
	{
		std::cout << a[i][3]<<"x^3 + "<< a[i][2]<<"x^2 + "<< a[i][1]<< "x + "<< a[i][0] << std::endl;
	}
		
	
	//STIMMT

	// cleanup
	for (int i=0; i<n-1; i++)
		delete [] matrix[i];
	delete [] matrix;
	delete [] sol;
	delete [] rhs;
}