Comprehensive Interpretation of a Three-Point Gauss Quadrature with Variable Sampling Points and Its Application to Integration for Discrete Data

Figure 1

Various sets of integration weights and optimal sampling points with respect to the weight ratio 𝜑; (a) 𝜑=0, (b) 𝜑=𝜀, (c) 𝜑=1, (d) 𝜑=8/5, (e) 𝜑=2, (f) 𝜑=4, (g) 𝜑=22, (h) 𝜑=52, and (i) 𝜑=∞.