Although extrapolation intrinsically is a less stable task than interpolation, it can nevertheless in many cases be highly effective. In the context of FD methods, a common situation is to have numerical results for a sequence of step sizes h approaching h = 0, together with theoretical knowledge that the computed solution (pointwise) possesses a convergent Taylor expansion (with unknown coefficients) around h = 0. Extrapolation down to h = 0 is then well posed and is known as Richardson extrapolation. Deferred correction is another option that sometimes can provide several additional orders of accuracy from a lower-order scheme (described in Chapter 3). The two methods just mentioned can be characterized as linear. In other applications, such as accelerating slowly converging iterations and evaluations of infinite sums, nonlinear techniques are often more effective. Two such methods are briefly described here: Aitken extrapolation and conversion of truncated Taylor expansions to Padé rational form. Such methods can in certain contexts provide spectacularly effective extrapolations (although strict error analysis often is difficult or unavailable).