CUBIC SPLINE INTERPOLATION
A. S. Shvedov VANT. Ser. Metodiki i Programmy Chislennogo Resheniya Zadach Matematicheskoy Fiziki 1987. Вып.2. С. 2022.
A problem of deriving the cubic spline s ∈ c^{i} [a,b] assuming given values in given (support) points of the segment [a,b]. The problem is simple but very important for applications. A new way of deriving such splines is suggested which possesses the following properties. Firstly, the splines are monotonic between any two neigbouring support points. Secondly, the first and second spline derivatives (the latter are discontinuous in general) are upperbounded by associated separated differences derived by support points and spline values at those points.
