An algorithm for the construction of a nonnegative cubic spline (Q1975753)

In the paper the authors consider the extremum problem \[ \int_a^b [f''(x)]^2 dx \rightarrow \inf f(t_j) = y_j,\quad j \in 1,2,\dots,n,\quad f(x) > 0, x \in [a,b]. \] A version of the Dauner-Reinsch algorithm for the construction of a nonnegative cubic spline interpolating positiv values is developed in detail. In this algorithm, the values of the global spline and its second order derivatives are used in solving a local problem. The criterion for the choice of additional knots is established. The localization of the additional isolated knots is made more precise. The results of calculations for two examples that demonstrate the effects of flooring for the solution on the horizontal axis and sinking for the solution of the parametric problem are presented.