Error estimates and convergence rates for variational Hermite interpolation (Q1273412)

Let \(E^{'}_r\) be a dual space to \(C^r(\mathbb R^d)\) and \(\Lambda=\{l_1,\dots,l_N\}\subseteq E_r^{'}\). The authors consider the \(h\)-spline Hermite interpolant \[ s(x)=\sum_{i=1}^N a_i*h(x)+\sum_{| j| <m}b_j x^j, \] satisfying \((L_i,s)=f_i\), \(1\leq i\leq n\), and \(\sum_{i=1}^{n}a_i(L_i,p)=0\) for polynomials \(p\) of degree less than \(m\). Assume that \(Y_j=\{y\in\mathbb R^d| D^j\sigma_y\in \Lambda\}\) and \(dist(Y_j,\omega)\leq \rho\). Then if \(M=D^k\delta_y\) for some \(k\in \mathbb Z^d\) such that \(| k| \leq r\), \(j\leq k\) and \(y\in\Omega\), we have \(| (M,f_s)| \leq C\rho^{r-| k| } \).