Cubic spline interpolation is among one of the most used methods for interpolating between data points where the arguments are organized as ascending series. In the library program we supply such a function, based on the so-called cubic spline method to be described below.

A spline function consists of polynomial pieces defined on subintervals. The different subintervals are connected via various continuity relations.

Assume we have at our disposal \( n+1 \) points \( x_0, x_1, \dots x_n \) arranged so that \( x_0 < x_1 < x_2 < \dots x_{n-1} < x_n \) (such points are called knots). A spline function \( s \) of degree \( k \) with \( n+1 \) knots is defined as follows

• On every subinterval \( [x_{i-1},x_i) \) s is a polynomial of degree \( \le k \).
• \( s \) has \( k-1 \) continuous derivatives in the whole interval \( [x_0,x_n] \).