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

Table 2

Relative errors of the different types of 3-point Gauss integration of variable sampling pints for 5 monomial integrands.

Weight ratio (φ)	Relative errors for each monomial integrand
	𝑥^1	𝑥^2	𝑥^3	𝑥^4	𝑥^5
0	0.0000𝐸+00	0.8974𝐸−08	0.1795𝐸−07	0.2778E  −  01	0.8333E  −  01
𝜀	0.0000𝐸+00	0.1761𝐸−07	0.3522𝐸−07	0.2778E  −  01	0.8333E  −  01
1	0.0000𝐸+00	0.1228𝐸−07	0.2456𝐸−07	0.1042E  −  01	0.3125E  −  01
8/5	0.0000𝐸+00	0.1264𝐸−07	0.2528𝐸−07	0.3829𝐸−07	0.5168𝐸−07
2	0.0000𝐸+00	0.1830𝐸−07	0.3661𝐸−07	0.6944E  −  02	0.2083  −  E01
4	0.0000𝐸+00	0.1490𝐸−07	0.2980𝐸−07	0.4167E  −  01	0.1250E  +  00
22	0.0000𝐸+00	0.1192𝐸−06	0.2384𝐸−06	0.3542E  +  00	0.1063E  +  01
52	0.0000𝐸+00	0.2533𝐸−06	0.5066𝐸−06	0.8750E  +  00	0.2625E  +  01
∞	0.0000𝐸+00	0.2500E  +  00	0.5000E  +  00	0.6875E  +  00	0.8125E  +  00

The italic numbers mean improper results.