What limits the DE precision?
For moderate sized problems several large eigenmatrix problems are solved together with several large matrix inverses. Although the algorithms used are ‘industry standard’ and highly optimized, roundoff, and multiply-accumulate errors get propagated through to the solution. A DE>1 is nonphysical and indicates that something has gone wrong (energy is conserved by this algorithm implementation so the SUM of the DEs should = 1). The easiest way to estimate the rate of convergence, and to get a handle on the numerical accuracy of the solution is to pick a representative point in the grating parameter space, and calculation the DE as a function of ORDERS only. A plot of DE vs. ORDERS retained will give an illustration of the convergence properties of the solution. Sometimes, when a DE>1 is encounter a very small change in the parameters, and/or increasing or decreasing the number of orders is sufficient to get the algorithm to behave itself. The rate of convergence is physically tied to the
