A new quadrature scheme based on an Extended Lagrange Interpolation process

A mixed scheme of product integration rules in (−1,1)

“…. By f (9) uϕ 9 ∞ ∼ 2e+12, for m = 256 the theoretical estimate assures 11 digits, while the effective digits are 15 (Table 3).…”

“…Now we show how to compute GMMs starting from the ordinary modified moments (MMs) {M j (y)} j defined in (9). Just for the sake of simplicity, we treat the Gegenbauer case w = v α,α , since the case α = β can be handled analogously.…”

“…Extended interpolation processes have been extensively studied from several authors, in bounded and unbounded intervals, and with estimates of the error in different norms (see for instance [1], [2], [3], [4], [5], [6], [7]). Recently an application in quadrature has been proposed in [8], [9].…”