(0, 1, 2, 4)interpolation by \(G\)-splines (Q1176047)

Given a uniform partition \(0=x_ 0<x_ 1<\dots<x_{n-1}<x_ n=1\) of the interval \([0,1]\) and real numbers \(\{y_ k,y_ k',y_ k'',y^{(4)}_ k\}^ n_{k=0}\), find \(s\) in a suitable class such that \(s^{(q)}(x_ k)=y^{(q)}_ k\), \(q=0,1,2,4\), \(k=0,\dots,n\). The author finds the solution in the class of deficient \(g\)-splines \(S^{*(2)}_{n,6}\) for \(f\in C^ 6\) and in \(S^{(2,g)}_{n,7}\) for \(f\in C^ 7\). Existence, uniqueness, error bounds and an application to differential equations are discussed.