Quadratic convergence of an extrapolation method

Extrapolation methods serve to accelerate the convergence of iteration processes like nonlinear programming or root finding. These methods are mostly genealizations of wellknown one dimensional schemes whose favourable properties are expected to be retained in several dimensions. Such an important property is quadratic acceleration which is the central topic of this paper. The acceleration property is demonstrated on a simple gradient method and the result is compared to direct application of more advanced iteration methods.