Piecewise \(L\)-splines of order 4: interpolation and \(L^{2}\) error bounds for splines in tension
Piecewise L-splines are generalizations of L-splines in the sense that they satisfy different differential equations in different mesh intervals. The authors correct the erroneous results in [\textit{P. M. Prenter}, Numer. Math. 18, 243--253 (1971; Zbl 0227.65012)] for a certain family of piecewise L-splines of order 4. They prove existence and uniqueness and obtain the first and second integral relations. These results are used to obtain \(L^{2}\) error bounds for interpolation using splines in tension. Error bounds, for derivatives are also given.
scientific article; zbMATH DE number 5655028