The Lagrange interpolation is a classical technique for performing interpolation. Sometimes this interpolation is also called the polynomial interpolation. In the first order approximation, it reduces to a linear interpolation, a concept also applied in (see Cubic Spline Method).

Algorithm Creation

For a given set of n + 1 data points (x₀,y₀),(x₁,y₁),..., (x_n,y_n), where no two x_i are the same, the interpolation polynomial in the Lagrange form is a linear combination:

Testing the Lagrange Method

In order to test the Lagrange method as defined above, a new TestLagrange() static method has been added and executed. Supporting code and methods are not shown.

           static void TestLagrange();
              {
                 ListBox1.Items.Clear();
                 ListBox2.Items.Clear();
                 double[] xarray = new double[] { t1, t2, t3, t4, t5 };
                 double[] yarray = new double[] { t6, t7, t8, t9, t10 };
                 double[] x = new double[] { t11, t12, t13 };
                 double[] y = Interpolation.Lagrange(xarray, yarray, x);
                 VectorR vx = new VectorR(x);
                 VectorR vy = new VectorR(y);
                 ListBox1.Items.Add(" " + vx.ToString());
                 ListBox2.Items.Add(" " + vy.ToString());
              }