Interpolation and Extrapolation

This volume is dedicated to two closely related subjects: interpolation and extrapolation. The papers can be divided into three categories: historical papers, survey papers and papers presenting new developments. Interpolation is an old subject since, as noticed in the paper by M. Gasca and T. Sauer, the term was coined by John Wallis in 1655. Interpolation was the first technique for obtaining an approximation of a function. Polynomial interpolation was then used in quadrature methods and methods for the numerical solution of ordinary differential equations. Extrapolation is based on interpolation. In fact, extrapolation consists of interpolation at a point outside the interval containing the interpolation points. Usually, this point is either zero or infinity. Extrapolation is used in numerical analysis to improve the accuracy of a process depending of a parameter or to accelerate the convergence of a sequence. The most well-known extrapolation processes are certainly Romberg's method for improving the convergence of the trapezoidal rule for the computation of a definite integral and Aiken's D2 process which can be found in any textbook of numerical analysis. Obviously, all aspects of interpolation and extrapolation have not been treated in this volume. However, many important topics have been covered.