Thus an invertible matrix equation is generated. Care must be taken to use an appropriate value for h; the simplest method is to factor the h terms out with the functions. Otherwise, for longer operators the matrix can be numerically unstable and difficult to invert. The h terms contribute to a poor condition number matrix. The result is general and will generate difference operators for any length.
Solving Equation 37 for the and derivative terms gives
If we modify the matrix terms by factoring out the terms in h in Equation 37, we get a simpler matrix which will have a better condition number: