Interpolation Aitken method

This method is used to interpolate not equispaced data

f(x) = { (x_i , y_i)   i = 0, 1, ... n }

This method is efficient as the Newton formula, but it is more easy to implement with computer program.

The interpolation value y_p = f(x_p) at a given point x_p, can be computed by the following iterative algorithm:

A simple Visual Basic code routine implementing this algorithm is:

Sub Interpolaz_Aitken(ByVal yi(), ByVal xi(), xp, yp)

'perform the aitken interpolation among n (xi,yi) points

'retuns yp= interpolation at xp

n = UBound(yi)

For j = 1 To n - 1

    For i = j + 1 To n

        y(i) = (y(j) * (x(i) - xp) - y(i) * (x(j) - xp)) / (x(i) - x(j))

    Next i

Next j

yp = y(n)

End Sub

Example: A function is known by the following table . Find the interpolate values for 0 < x < 4 with step h = 0.2

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