On the ideal weights for WENO/WENO-like finite difference schemes for the first derivative, I

An interesting fact which was used in the construction of targeted essentially non-oscillatory (TENO) schemes is that a [Formula: see text]th order accurate scheme can be written as a linear combination of two [Formula: see text]th order accurate schemes. Taking advantage of this fact, we propose a formula to determine the ideal weights used in developing finite difference WENO/WENO-like schemes. Such quantitative results are helpful for further discussion on finite difference WENO/WENO-like schemes.