Suppose that we have $n$ uniformly separated points (assume separation of 1), with $k$ derivatives at each point, resulting in $nk$ number of data. But each data has known measurement error bound. For simplification, assume that every data of $i$th derivative has the same error magnitude upper bound but $j$th derivative data have different error magnitude upper bound. ($i \neq j$) And we perform Hermite interpolation on these data.
Is there any known resulting interpolation error formula, given error bound for each data?