The k function values are to be interpolated by a piecewise cubic spline. The k-1 cubic polynomials are defined on the intervals [xi,xi+1],i ∈ {1,...,k-1}. Indicate which of the following statements apply in general.
For each spline interval, a system of equations is set up, solved and thus the polynomial for the interval is determined.
The system matrix for calculating the cubic spline is singular if xi=xj, i≠j.
I think the first statement is not true and the second is, but I would like to be sure.