Mathematical research
1 total work
Vol 88
Extrapolation methods are used to accelerate the convergence of a given sequence of numbers, vectors or matrices. They play an important role in many branches of numerical analysis, such as approximation of functions, numerical integration, or discretization methods for ODEs. This text provides a detailed survey of linear extrapolation methods, investigates their properties and efficiency, and establishes some generalizations about them. The applicability of extrapolation methods is connected with the existence of an asymptotic expansion of the sequence under consideration. The first part of the book is therefore devoted to the investigation of asymptotic expansions and their appearance in very different fields.