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

Table 4

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

𝑟	Integral 3			Integral 4
	Anderson	Pravin	Improved	Anderson	Pravin	Improved
1.00𝐸−04	2.18𝐸−07	4.39𝐸−04	4.60𝐸−09	3.64𝐸−07	3.71𝐸−08	5.11𝐸−08
1.00𝐸−03	0.00𝐸+00	4.39𝐸−04	4.60𝐸−09	3.64𝐸−07	4.08𝐸−08	5.11𝐸−08
5.00𝐸−03	2.79𝐸−07	4.39𝐸−04	4.60𝐸−09	3.64𝐸−07	4.06𝐸−08	5.11𝐸−08
1.00𝐸−02	1.86𝐸−07	4.37𝐸−04	4.60𝐸−09	3.64𝐸−07	4.04𝐸−08	5.11𝐸−08
5.00𝐸−02	2.24𝐸−07	3.80𝐸−04	4.61𝐸−09	3.64𝐸−07	3.50𝐸−08	5.11𝐸−08
1.00𝐸−01	1.49𝐸−07	2.37𝐸−04	4.61𝐸−09	3.64𝐸−07	2.14𝐸−08	5.13𝐸−08
5.00𝐸−01	1.27𝐸−07	5.11𝐸−06	4.86𝐸−09	3.64𝐸−07	3.30𝐸−10	5.62𝐸−08
1.00𝐸+00	2.45𝐸−06	1.39𝐸−06	5.83𝐸−09	3.64𝐸−07	1.14𝐸−10	6.63𝐸−08
2.00𝐸+00	5.91𝐸−06	7.36𝐸−07	1.21𝐸−08	3.64𝐸−07	2.71𝐸−11	7.65𝐸−08