APPROXIMATION FORMULAE GENERATED BY EXPONENTIAL FITTING

We present the main elements of the exponential fitting techniquefor building up linear approximation formulae. We cover the two maincomponents of this technique, that is the error analysis and the wayin which the coefficients of the new formulae can be determined. Wepresent briefly the recently developed error analysis of Coleman andIxaru, whose main result is that the error of the formulae based on the exponential fitting (ef, for short) is a sum of two Lagrange-like terms, in contrast to the case of the classical formulae where it consists of a single term. For application we consider the case of two quadrature formulae (extended Newton-Cotes and Gauss), which are indistinguishable in the frame of the traditional error analysis, to find out that the Gauss rule is more accurate. As for the determination of the coefficients, we show how the ef procedure can be applied for deriving formulae of classical type. We re-obtain wellknown formulae and also derive some new ones.