Abstract
Numerical methods using derivatives have been considered until recently to be disadvantageous. However, since automatic methods for simultaneous computation of functions and partial derivatives are now available, we may make more use of derivatives in various fields of numerical methods. From this standpoint, we consider the complexity of new variants of the Romberg integration, which require the derivatives only at both endpoints. Among these variants, the method using the first derivatives is one of the most promising with respect to the amount of computational work, because it achieves the same accuracy as the standard Romberg integration with half stepsize.
