Backward Interpolation.java

// Backward Interpolation
class InterpolateBackward {

// Calculation of u mentioned in formula

static double u_cal(double u, int n)
{
	double temp = u;
	for (int i = 1; i < n; i++)
		temp = temp * (u + i);
	return temp;
}

// Calculating factorial of given n

static int fact(int n)
{
	int f = 1;
	for (int i = 2; i <= n; i++)
		f *= i;
	return f;
}

public static void main(String[] args) {

	int n = 4; // Manual Input
	double x[] = { 1, 3, 5, 7}; // Manual Input the equation, y0,y1,y2,y3.......

	// table and y[][0] are used for input

	double[][] y = new double[n][n];
	y[0][0] = 3;
	y[1][0] = 14;
	y[2][0] = 19;
	y[3][0] = 21;
	// y[4][0] = 101;
	//......

	// Calculating the backward difference table

	for (int i = 1; i < n; i++)
	{
		for (int j = n - 1; j >= i; j--)
			y[j][i] = y[j][i - 1] - y[j - 1][i - 1];
	}

	// Displaying the backward difference table

	for (int i = 0; i < n; i++)
	{
		for (int j = 0; j <= i; j++)
			System.out.print(y[i][j] + "\t");
		System.out.println("");;
	}

	// Value to interpolate at

	double value = 4;

	// Initializing u and sum

	double sum = y[n - 1][0];
	double u = (value - x[n - 1]) / (x[1] - x[0]);
	for (int i = 1; i < n; i++)
	{
		sum = sum + (u_cal(u, i) * y[n - 1][i]) / fact(i);
	}
	System.out.println("\n Value of Y at " + value + " is " + String.format("%.6g%n",sum)); //Answer
}
}