It was found that all the six algorithms reproduced a void fraction of precisely 0.34.The algorithms however different CPU time, errors, and error distribution.
The three different error norms reported in the present work are:

Maximum of absolute difference

Table 11: Comparison of the MART Algorithms: Circular Region with Holes

Quantity	MART1	MART2	MART3	AVMART1	AVMART2	AVMART3
	0.99	0.96	0.95	0.99	0.96	0.96
	0.25	0.24	0.23	0.24	0.23	0.23
	25.12	24.08	23.63	24.59	23.72	23.65
Number of points (%) having error in the range
>95%	0.27	0.05	0.05	0.27	0.05	0.05
75-95%	0.64	0.62	0.86	0.83	0.72	0.70
50-75%	3.90	4.11	4.43	3.47	4.00	3.98
Iterations	51	63	29	17	24	21
CPU (minutes)	9.51	11.97	5.65	0.32	0.45	0.40

Results for the error level distribution in the reconstructed field have also determined. The distribution of the absolute error as a percentage of the error has been presented in the regions Errors and their distribution along with the computational details are given in Table 11.
It is clear form Table 11 that the errors for all the six algorithms are practically close, with those of MART 1 and AVMART 1 being marginally on the higher side. An examination of the error distribution shows that large error (>95%) are seen only over of the physical region shows that large errors are seen only over 27% of the physical region. Specifically, large errors are restricted to the surface of the holes, where a step change in the field property (the density in the present example) takes place. The errors are uniformly small elsewhere. The most significant difference between the original and the proposed algorithms is in terms of the number of iterations (and correspondingly in the CPU time). The proposed algorithms require less iteration for convergence and require a smaller CPU time. This is clear evidence of the computational efficiency of the proposed algorithms in the context of exact projection data.