Exercises

1.  Neville's Algorithm and Cubic Spline

Given the following table of values,

a.  Neville's Algorithm

The interpolating polynomial of least degree is p (x) = 3x⁴ +2x³ - 7x² + 4x -5. Using Neville's algorithm, find the interpolated value at x = 1.5 and the error estimate. Compare the error estimate with the estimate obtained using p(x) above (the difference between the value calculated and the value given by the polynomial).

b.  Cubic Spline

Find the interpolated value at x = 1.5 using the cublic spline approach. Is it closer to the value predicted by an evaluation of the polynomial?

2.  Interpolating Polynomial

Use the same data as provided above.

Find the coefficients of the interpolating polynomial

Using the polynomial, calculate the interpolated value at x = 1.5.

3.  Graphics

Graph the interpolating polynomial given in part 1a above. Draw some conclusions concerning the interpolated value obtained in part 1b using the cublic spline approach.