Spline Interpolation - Example

Example

In case of three points the values for are found by solving the linear equation system

\begin{bmatrix} a_{11} & a_{12} & 0 \\ a_{21} & a_{22} & a_{23} \\ 0 & a_{32} & a_{33} \\ \end{bmatrix} \begin{bmatrix} k_0 \\ k_1 \\ k_2 \\ \end{bmatrix} = \begin{bmatrix} b_1 \\ b_2 \\ b_3 \\ \end{bmatrix}

with

For the three points

one gets that

and from (10) and (11) that

In Figure 2 the spline function consisting of the two cubic polynomials and given by (9) is displayed

Read more about this topic:  Spline Interpolation

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