Iterative Scheme for Solving Optimal Transportation Problems Arising in Reflector Design

Table 3

Results of the final iteration of the “Iterative Refinement” Scheme 6 with different values of the nearest neighbor search depth 𝜅_nn. All other data used was the same as in Table 2. Note that the nearest neighbor search depth 𝜅_nn has a large influence on the size of the LP problem but relatively little influence on the errors or run times. Column labels are identical to Table 2 except for the first column.

𝜅nn	ℎ	𝑀	𝑁	Max error 𝑅1	𝐿2 error 𝑅1	Max error 𝑅2	𝐿2 error 𝑅2	Constr.	Con. dens.	Time (s)	LP time (s)
2	0.02097152	10,313	10,318	2.71973𝐸−4	9.04017𝐸−5	4.38374𝐸−4	1.37601𝐸−4	96256	0.090%	5947.76	2.82425
4	0.02097152	10,313	10,318	2.48492𝐸−4	9.77635𝐸−5	3.92226𝐸−4	1.50005𝐸−4	226006	0.212%	5752.17	6.09849
6	0.02097152	10,313	10,318	2.49854𝐸−4	9.9045𝐸−5	3.9372𝐸−4	1.51851𝐸−4	351514	0.330%	5909.25	9.21891
8	0.02097152	10,313	10,318	2.49816𝐸−4	9.90729𝐸−5	3.94393𝐸−4	1.5188𝐸−4	482058	0.453%	6322.4	12.9115