Roundoff (truncation) errors

Round-off error is due to the fact that real numbers are represented by binary number approximations in a computer. This effect is complementary to the other error sources, since it accumulates with the total number of floating-point operations, and therefore gets larger when the step-sizes are reduced--or as the spatial window is increased. This effect is often ignored, under the assumption that commonly used double-precision floating-point IEEE operations (64bit, 16-17 decimals) have negligible round-off errors. However, for very accurate calculations with large lattices, this effect can become important. With some computer languages, it is possible to repeat the calculation with quadruple-precision (128bit, 32-34 decimals). If the calculations give results that differ by more than the error tolerance at two different precisions, then round-off is clearly a problem.