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 "Interpolation Solutions" Lagrange Method
 X = (2, 3, 1)
 Y = (4, 9, 1)

 Array X = { , , , , } Array Y = { , , , , } Specify New X values = { , , } [ Initial ArrayValues X: {1,2,3,4,5} ] [ Initial ArrayValues Y: {1,4,9,16,25} ] [ Initial LagrangeX Values specified: {2,3,1} ]

IMPLEMENTATION
Lagrange Interpolation

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),..., (xn,yn), where no two xi are the same, the interpolation polynomial in the Lagrange form is a linear combination:

 y = f(x) = ∑i=0n li(x) f(xi) 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);
}

We first defined a set of data points as xarray and yarray. We then compute the y values at the xLagrange values specified. The user can manipulate all values and try variations on the arrays themselves as well as specifying new xLagrange values.

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