Fast Hankel Transforms Algorithm Based on Kernel Function Interpolation with Exponential Functions

Table 3

Relative error comparison among Anderson, Pravin, and improved method for zero-order HT.

𝑟	Integral 1			Integral 2
	Anderson	Pravin	Improved	Anderson	Pravin	Improved
1.00𝐸−04	1.07𝐸−06	6.38𝐸−06	2.73𝐸−08	2.81𝐸−05	2.76𝐸−10	3.04𝐸−07
1.00𝐸−03	4.77𝐸−07	6.38𝐸−06	2.73𝐸−08	2.62𝐸−06	2.76𝐸−10	3.04𝐸−07
5.00𝐸−03	1.07𝐸−07	6.37𝐸−06	2.73𝐸−08	5.96𝐸−07	2.75𝐸−10	3.04𝐸−07
1.00𝐸−02	1.10𝐸−07	6.33𝐸−06	2.73𝐸−08	7.15𝐸−07	2.73𝐸−10	3.04𝐸−07
5.00𝐸−02	1.19𝐸−07	5.14𝐸−06	2.73𝐸−08	2.38𝐸−07	2.05𝐸−10	3.04𝐸−07
1.00𝐸−01	1.20𝐸−07	2.42𝐸−06	2.73𝐸−08	1.19𝐸−07	5.06𝐸−10	3.04𝐸−07
5.00𝐸−01	1.27𝐸−07	1.09𝐸−06	2.74𝐸−08	0.00𝐸+00	2.79𝐸−10	3.14𝐸−07
1.00𝐸+00	3.83𝐸−07	1.79𝐸−06	2.84𝐸−08	2.67𝐸−07	6.50𝐸−10	3.50𝐸−07
2.00𝐸+00	1.86𝐸−06	3.80𝐸−06	4.08𝐸−08	8.43𝐸−07	7.16𝐸−10	4.65𝐸−07