JEOS RP ISSN03 | Page 330

J. Eur. Opt. Society-Rapid Publ. 22, 31( 2026) 323
Table B2. The inverse transformation matrix T �1, up to order 6, with 2 decimal digits for visualization.
0 1 2 3 4 5 6 m = i 0 0 1 0 1 2 0 1 2 3 0 1 2 3 4 0 1 2 3 4 5 0 1 2 3 4 5 6
0 0 1.00 0
0 0.25 0
0.25
0
0
0
0
0.13 0
0.04
0
0.13
0
0
0
0
0
0
0.08 0
0.02
0
0.02
0
0.08
1 �1
0
0 1.00 0
0
0
0 0.17
0
0.50
0
0
0
0
0
0 0.06
0
0.06
0
0.31
0
0
0
0
0
0
0
1
0 1.00 0
0
0
0
0.50 0
0.17
0
0
0
0
0
0
0.31 0
0.06
0
0.06
0
0
0
0
0
0
0
0
2 �2
0
0
0
0 0.50
0
0
0
0
0
0 0.19
0
0.19
0
0
0
0
0
0
0
0 0.09
0
0.06
0
0.09
0
0
0
0
0 0.25 0
0.25
0
0
0
0
0.19 0
0.06
0
0.19
0
0
0
0
0
0
0.14 0
0.03
0
0.03
0
0.14
2
0
0
0 0.50 0 �0.50 0
0
0
0
0.38 0
0.00
0
�0.38 0
0
0
0
0
0
0.28 0
0.02
0
�0.02
0
�0.28
3 �3
0
0
0
0
0
0
0 0.25
0
�0.25 0
0
0
0
0
0 0.15
0
0.05
0
�0.25 0
0
0
0
0
0
0
�1
0
0
0
0
0
0
0 0.08
0
0.25
0
0
0
0
0
0 0.05
0
0.05
0
0.25
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0.25 0
0.08
0
0
0
0
0
0
0.25 0
0.05
0
0.05
0
0
0
0
0
0
0
0
3
0
0
0
0
0
0
0.25 0 �0.25
0
0
0
0
0
0
0.25 0 �0.05
0
�0.15
0
0
0
0
0
0
0
0
4 �4
0
0
0
0
0
0
0
0
0
0
0 0.13
0
�0.13
0
0
0
0
0
0
0
0 0.10
0
0.00
0
�0.10
0
�2
0
0
0
0
0
0
0
0
0
0
0 0.06
0
0.06
0
0
0
0
0
0
0
0 0.05
0
0.03
0
0.05
0
0
0
0
0
0
0
0
0
0
0
0
0.06 0
0.02
0
0.06
0
0
0
0
0
0
0.08 0
0.02
0
0.02
0
0.08
2
0
0
0
0
0
0
0
0
0
0
0.13 0
0.00
0
�0.13 0
0
0
0
0
0
0.16 0
0.01
0
�0.01
0
�0.16
4
0
0
0
0
0
0
0
0
0
0
0.13 0 �0.13
0
0.13
0
0
0
0
0
0
0.16 0 �0.05
0
�0.05
0
0.16
5 �5
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0 0.06
0
�0.06
0
0.06
0
0
0
0
0
0
0
�3
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0 0.04
0
0.01
0
�0.06 0
0
0
0
0
0
0
�1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0 0.01
0
0.01
0
0.06
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0.06 0
0.01
0
0.01
0
0
0
0
0
0
0
0
3
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0.06 0 �0.01
0
�0.04
0
0
0
0
0
0
0
0
5
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0.06 0 �0.06
0
0.06
0
0
0
0
0
0
0
0
6 �6
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0 0.03
0
�0.03
0
0.03
0
�4
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0 0.02
0
0.00
0
�0.02
0
�2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0 0.01
0
0.01
0
0.01
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0.02 0
0.00
0
0.00
0
0.02
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0.03 0
0.00
0
0.00
0
�0.03
4
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0.03 0 �0.01
0
�0.01
0
0.03
6
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0.03 0 �0.03
0
0.03
0
�0.03