% Following are the nonzeros in the Poisson matrix A with k = 4. % A is a n n-by-n matrix where n = k^3 = 64. (1,1) 6 (2,1) -1 (5,1) -1 (17,1) -1 (1,2) -1 (2,2) 6 (3,2) -1 (6,2) -1 (18,2) -1 (2,3) -1 (3,3) 6 (4,3) -1 (7,3) -1 (19,3) -1 (3,4) -1 (4,4) 6 (8,4) -1 (20,4) -1 (1,5) -1 (5,5) 6 (6,5) -1 (9,5) -1 (21,5) -1 (2,6) -1 (5,6) -1 (6,6) 6 (7,6) -1 (10,6) -1 (22,6) -1 (3,7) -1 (6,7) -1 (7,7) 6 (8,7) -1 (11,7) -1 (23,7) -1 (4,8) -1 (7,8) -1 (8,8) 6 (12,8) -1 (24,8) -1 (5,9) -1 (9,9) 6 (10,9) -1 (13,9) -1 (25,9) -1 (6,10) -1 (9,10) -1 (10,10) 6 (11,10) -1 (14,10) -1 (26,10) -1 (7,11) -1 (10,11) -1 (11,11) 6 (12,11) -1 (15,11) -1 (27,11) -1 (8,12) -1 (11,12) -1 (12,12) 6 (16,12) -1 (28,12) -1 (9,13) -1 (13,13) 6 (14,13) -1 (29,13) -1 (10,14) -1 (13,14) -1 (14,14) 6 (15,14) -1 (30,14) -1 (11,15) -1 (14,15) -1 (15,15) 6 (16,15) -1 (31,15) -1 (12,16) -1 (15,16) -1 (16,16) 6 (32,16) -1 (1,17) -1 (17,17) 6 (18,17) -1 (21,17) -1 (33,17) -1 (2,18) -1 (17,18) -1 (18,18) 6 (19,18) -1 (22,18) -1 (34,18) -1 (3,19) -1 (18,19) -1 (19,19) 6 (20,19) -1 (23,19) -1 (35,19) -1 (4,20) -1 (19,20) -1 (20,20) 6 (24,20) -1 (36,20) -1 (5,21) -1 (17,21) -1 (21,21) 6 (22,21) -1 (25,21) -1 (37,21) -1 (6,22) -1 (18,22) -1 (21,22) -1 (22,22) 6 (23,22) -1 (26,22) -1 (38,22) -1 (7,23) -1 (19,23) -1 (22,23) -1 (23,23) 6 (24,23) -1 (27,23) -1 (39,23) -1 (8,24) -1 (20,24) -1 (23,24) -1 (24,24) 6 (28,24) -1 (40,24) -1 (9,25) -1 (21,25) -1 (25,25) 6 (26,25) -1 (29,25) -1 (41,25) -1 (10,26) -1 (22,26) -1 (25,26) -1 (26,26) 6 (27,26) -1 (30,26) -1 (42,26) -1 (11,27) -1 (23,27) -1 (26,27) -1 (27,27) 6 (28,27) -1 (31,27) -1 (43,27) -1 (12,28) -1 (24,28) -1 (27,28) -1 (28,28) 6 (32,28) -1 (44,28) -1 (13,29) -1 (25,29) -1 (29,29) 6 (30,29) -1 (45,29) -1 (14,30) -1 (26,30) -1 (29,30) -1 (30,30) 6 (31,30) -1 (46,30) -1 (15,31) -1 (27,31) -1 (30,31) -1 (31,31) 6 (32,31) -1 (47,31) -1 (16,32) -1 (28,32) -1 (31,32) -1 (32,32) 6 (48,32) -1 (17,33) -1 (33,33) 6 (34,33) -1 (37,33) -1 (49,33) -1 (18,34) -1 (33,34) -1 (34,34) 6 (35,34) -1 (38,34) -1 (50,34) -1 (19,35) -1 (34,35) -1 (35,35) 6 (36,35) -1 (39,35) -1 (51,35) -1 (20,36) -1 (35,36) -1 (36,36) 6 (40,36) -1 (52,36) -1 (21,37) -1 (33,37) -1 (37,37) 6 (38,37) -1 (41,37) -1 (53,37) -1 (22,38) -1 (34,38) -1 (37,38) -1 (38,38) 6 (39,38) -1 (42,38) -1 (54,38) -1 (23,39) -1 (35,39) -1 (38,39) -1 (39,39) 6 (40,39) -1 (43,39) -1 (55,39) -1 (24,40) -1 (36,40) -1 (39,40) -1 (40,40) 6 (44,40) -1 (56,40) -1 (25,41) -1 (37,41) -1 (41,41) 6 (42,41) -1 (45,41) -1 (57,41) -1 (26,42) -1 (38,42) -1 (41,42) -1 (42,42) 6 (43,42) -1 (46,42) -1 (58,42) -1 (27,43) -1 (39,43) -1 (42,43) -1 (43,43) 6 (44,43) -1 (47,43) -1 (59,43) -1 (28,44) -1 (40,44) -1 (43,44) -1 (44,44) 6 (48,44) -1 (60,44) -1 (29,45) -1 (41,45) -1 (45,45) 6 (46,45) -1 (61,45) -1 (30,46) -1 (42,46) -1 (45,46) -1 (46,46) 6 (47,46) -1 (62,46) -1 (31,47) -1 (43,47) -1 (46,47) -1 (47,47) 6 (48,47) -1 (63,47) -1 (32,48) -1 (44,48) -1 (47,48) -1 (48,48) 6 (64,48) -1 (33,49) -1 (49,49) 6 (50,49) -1 (53,49) -1 (34,50) -1 (49,50) -1 (50,50) 6 (51,50) -1 (54,50) -1 (35,51) -1 (50,51) -1 (51,51) 6 (52,51) -1 (55,51) -1 (36,52) -1 (51,52) -1 (52,52) 6 (56,52) -1 (37,53) -1 (49,53) -1 (53,53) 6 (54,53) -1 (57,53) -1 (38,54) -1 (50,54) -1 (53,54) -1 (54,54) 6 (55,54) -1 (58,54) -1 (39,55) -1 (51,55) -1 (54,55) -1 (55,55) 6 (56,55) -1 (59,55) -1 (40,56) -1 (52,56) -1 (55,56) -1 (56,56) 6 (60,56) -1 (41,57) -1 (53,57) -1 (57,57) 6 (58,57) -1 (61,57) -1 (42,58) -1 (54,58) -1 (57,58) -1 (58,58) 6 (59,58) -1 (62,58) -1 (43,59) -1 (55,59) -1 (58,59) -1 (59,59) 6 (60,59) -1 (63,59) -1 (44,60) -1 (56,60) -1 (59,60) -1 (60,60) 6 (64,60) -1 (45,61) -1 (57,61) -1 (61,61) 6 (62,61) -1 (46,62) -1 (58,62) -1 (61,62) -1 (62,62) 6 (63,62) -1 (47,63) -1 (59,63) -1 (62,63) -1 (63,63) 6 (64,63) -1 (48,64) -1 (60,64) -1 (63,64) -1 (64,64) 6 % Following is the whole Poisson matrix with k = 4. % A is a n n-by-n matrix where n = k^3 = 64. % Remember, your matrix data structure should not store the zeros. 6 -1 0 0 -1 0 0 0 0 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 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 -1 6 -1 0 0 -1 0 0 0 0 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 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 -1 6 -1 0 0 -1 0 0 0 0 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 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 -1 6 0 0 0 -1 0 0 0 0 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 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 -1 0 0 0 6 -1 0 0 -1 0 0 0 0 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 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 -1 0 0 -1 6 -1 0 0 -1 0 0 0 0 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 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 -1 0 0 -1 6 -1 0 0 -1 0 0 0 0 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 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 -1 0 0 -1 6 0 0 0 -1 0 0 0 0 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 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 -1 0 0 0 6 -1 0 0 -1 0 0 0 0 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 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 -1 0 0 -1 6 -1 0 0 -1 0 0 0 0 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 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 -1 0 0 -1 6 -1 0 0 -1 0 0 0 0 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 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 -1 0 0 -1 6 0 0 0 -1 0 0 0 0 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 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 -1 0 0 0 6 -1 0 0 0 0 0 0 0 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 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 -1 0 0 -1 6 -1 0 0 0 0 0 0 0 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 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 -1 0 0 -1 6 -1 0 0 0 0 0 0 0 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 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 -1 0 0 -1 6 0 0 0 0 0 0 0 0 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 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 -1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 6 -1 0 0 -1 0 0 0 0 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 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 -1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 -1 6 -1 0 0 -1 0 0 0 0 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 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 -1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 -1 6 -1 0 0 -1 0 0 0 0 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 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 -1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 -1 6 0 0 0 -1 0 0 0 0 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 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 -1 0 0 0 0 0 0 0 0 0 0 0 -1 0 0 0 6 -1 0 0 -1 0 0 0 0 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 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 -1 0 0 0 0 0 0 0 0 0 0 0 -1 0 0 -1 6 -1 0 0 -1 0 0 0 0 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 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 -1 0 0 0 0 0 0 0 0 0 0 0 -1 0 0 -1 6 -1 0 0 -1 0 0 0 0 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 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 -1 0 0 0 0 0 0 0 0 0 0 0 -1 0 0 -1 6 0 0 0 -1 0 0 0 0 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 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 -1 0 0 0 0 0 0 0 0 0 0 0 -1 0 0 0 6 -1 0 0 -1 0 0 0 0 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 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 -1 0 0 0 0 0 0 0 0 0 0 0 -1 0 0 -1 6 -1 0 0 -1 0 0 0 0 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 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 -1 0 0 0 0 0 0 0 0 0 0 0 -1 0 0 -1 6 -1 0 0 -1 0 0 0 0 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 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 -1 0 0 0 0 0 0 0 0 0 0 0 -1 0 0 -1 6 0 0 0 -1 0 0 0 0 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 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 -1 0 0 0 0 0 0 0 0 0 0 0 -1 0 0 0 6 -1 0 0 0 0 0 0 0 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 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 -1 0 0 0 0 0 0 0 0 0 0 0 -1 0 0 -1 6 -1 0 0 0 0 0 0 0 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 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 -1 0 0 0 0 0 0 0 0 0 0 0 -1 0 0 -1 6 -1 0 0 0 0 0 0 0 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 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 -1 0 0 0 0 0 0 0 0 0 0 0 -1 0 0 -1 6 0 0 0 0 0 0 0 0 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 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 -1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 6 -1 0 0 -1 0 0 0 0 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 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 -1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 -1 6 -1 0 0 -1 0 0 0 0 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 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 -1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 -1 6 -1 0 0 -1 0 0 0 0 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 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 -1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 -1 6 0 0 0 -1 0 0 0 0 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 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 -1 0 0 0 0 0 0 0 0 0 0 0 -1 0 0 0 6 -1 0 0 -1 0 0 0 0 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 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 -1 0 0 0 0 0 0 0 0 0 0 0 -1 0 0 -1 6 -1 0 0 -1 0 0 0 0 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 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 -1 0 0 0 0 0 0 0 0 0 0 0 -1 0 0 -1 6 -1 0 0 -1 0 0 0 0 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 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 -1 0 0 0 0 0 0 0 0 0 0 0 -1 0 0 -1 6 0 0 0 -1 0 0 0 0 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 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 -1 0 0 0 0 0 0 0 0 0 0 0 -1 0 0 0 6 -1 0 0 -1 0 0 0 0 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 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 -1 0 0 0 0 0 0 0 0 0 0 0 -1 0 0 -1 6 -1 0 0 -1 0 0 0 0 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 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 -1 0 0 0 0 0 0 0 0 0 0 0 -1 0 0 -1 6 -1 0 0 -1 0 0 0 0 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 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 -1 0 0 0 0 0 0 0 0 0 0 0 -1 0 0 -1 6 0 0 0 -1 0 0 0 0 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 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 -1 0 0 0 0 0 0 0 0 0 0 0 -1 0 0 0 6 -1 0 0 0 0 0 0 0 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 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 -1 0 0 0 0 0 0 0 0 0 0 0 -1 0 0 -1 6 -1 0 0 0 0 0 0 0 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 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 -1 0 0 0 0 0 0 0 0 0 0 0 -1 0 0 -1 6 -1 0 0 0 0 0 0 0 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 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 -1 0 0 0 0 0 0 0 0 0 0 0 -1 0 0 -1 6 0 0 0 0 0 0 0 0 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 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 -1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 6 -1 0 0 -1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 -1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 -1 6 -1 0 0 -1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 -1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 -1 6 -1 0 0 -1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 -1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 -1 6 0 0 0 -1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 -1 0 0 0 0 0 0 0 0 0 0 0 -1 0 0 0 6 -1 0 0 -1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 -1 0 0 0 0 0 0 0 0 0 0 0 -1 0 0 -1 6 -1 0 0 -1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 -1 0 0 0 0 0 0 0 0 0 0 0 -1 0 0 -1 6 -1 0 0 -1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 -1 0 0 0 0 0 0 0 0 0 0 0 -1 0 0 -1 6 0 0 0 -1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 -1 0 0 0 0 0 0 0 0 0 0 0 -1 0 0 0 6 -1 0 0 -1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 -1 0 0 0 0 0 0 0 0 0 0 0 -1 0 0 -1 6 -1 0 0 -1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 -1 0 0 0 0 0 0 0 0 0 0 0 -1 0 0 -1 6 -1 0 0 -1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 -1 0 0 0 0 0 0 0 0 0 0 0 -1 0 0 -1 6 0 0 0 -1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 -1 0 0 0 0 0 0 0 0 0 0 0 -1 0 0 0 6 -1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 -1 0 0 0 0 0 0 0 0 0 0 0 -1 0 0 -1 6 -1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 -1 0 0 0 0 0 0 0 0 0 0 0 -1 0 0 -1 6 -1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 -1 0 0 0 0 0 0 0 0 0 0 0 -1 0 0 -1 6 % Following are the nonzeros in the Poisson matrix A with k = 3. % A is a n n-by-n matrix where n = k^3 = 27. (1,1) 6 (2,1) -1 (4,1) -1 (10,1) -1 (1,2) -1 (2,2) 6 (3,2) -1 (5,2) -1 (11,2) -1 (2,3) -1 (3,3) 6 (6,3) -1 (12,3) -1 (1,4) -1 (4,4) 6 (5,4) -1 (7,4) -1 (13,4) -1 (2,5) -1 (4,5) -1 (5,5) 6 (6,5) -1 (8,5) -1 (14,5) -1 (3,6) -1 (5,6) -1 (6,6) 6 (9,6) -1 (15,6) -1 (4,7) -1 (7,7) 6 (8,7) -1 (16,7) -1 (5,8) -1 (7,8) -1 (8,8) 6 (9,8) -1 (17,8) -1 (6,9) -1 (8,9) -1 (9,9) 6 (18,9) -1 (1,10) -1 (10,10) 6 (11,10) -1 (13,10) -1 (19,10) -1 (2,11) -1 (10,11) -1 (11,11) 6 (12,11) -1 (14,11) -1 (20,11) -1 (3,12) -1 (11,12) -1 (12,12) 6 (15,12) -1 (21,12) -1 (4,13) -1 (10,13) -1 (13,13) 6 (14,13) -1 (16,13) -1 (22,13) -1 (5,14) -1 (11,14) -1 (13,14) -1 (14,14) 6 (15,14) -1 (17,14) -1 (23,14) -1 (6,15) -1 (12,15) -1 (14,15) -1 (15,15) 6 (18,15) -1 (24,15) -1 (7,16) -1 (13,16) -1 (16,16) 6 (17,16) -1 (25,16) -1 (8,17) -1 (14,17) -1 (16,17) -1 (17,17) 6 (18,17) -1 (26,17) -1 (9,18) -1 (15,18) -1 (17,18) -1 (18,18) 6 (27,18) -1 (10,19) -1 (19,19) 6 (20,19) -1 (22,19) -1 (11,20) -1 (19,20) -1 (20,20) 6 (21,20) -1 (23,20) -1 (12,21) -1 (20,21) -1 (21,21) 6 (24,21) -1 (13,22) -1 (19,22) -1 (22,22) 6 (23,22) -1 (25,22) -1 (14,23) -1 (20,23) -1 (22,23) -1 (23,23) 6 (24,23) -1 (26,23) -1 (15,24) -1 (21,24) -1 (23,24) -1 (24,24) 6 (27,24) -1 (16,25) -1 (22,25) -1 (25,25) 6 (26,25) -1 (17,26) -1 (23,26) -1 (25,26) -1 (26,26) 6 (27,26) -1 (18,27) -1 (24,27) -1 (26,27) -1 (27,27) 6 % Following is the whole Poisson matrix with k = 3. % A is a n n-by-n matrix where n = k^3 = 27. % Remember, your matrix data structure should not store the zeros. 6 -1 0 -1 0 0 0 0 0 -1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 -1 6 -1 0 -1 0 0 0 0 0 -1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 -1 6 0 0 -1 0 0 0 0 0 -1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 -1 0 0 6 -1 0 -1 0 0 0 0 0 -1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 -1 0 -1 6 -1 0 -1 0 0 0 0 0 -1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 -1 0 -1 6 0 0 -1 0 0 0 0 0 -1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 -1 0 0 6 -1 0 0 0 0 0 0 0 -1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 -1 0 -1 6 -1 0 0 0 0 0 0 0 -1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 -1 0 -1 6 0 0 0 0 0 0 0 0 -1 0 0 0 0 0 0 0 0 0 -1 0 0 0 0 0 0 0 0 6 -1 0 -1 0 0 0 0 0 -1 0 0 0 0 0 0 0 0 0 -1 0 0 0 0 0 0 0 -1 6 -1 0 -1 0 0 0 0 0 -1 0 0 0 0 0 0 0 0 0 -1 0 0 0 0 0 0 0 -1 6 0 0 -1 0 0 0 0 0 -1 0 0 0 0 0 0 0 0 0 -1 0 0 0 0 0 -1 0 0 6 -1 0 -1 0 0 0 0 0 -1 0 0 0 0 0 0 0 0 0 -1 0 0 0 0 0 -1 0 -1 6 -1 0 -1 0 0 0 0 0 -1 0 0 0 0 0 0 0 0 0 -1 0 0 0 0 0 -1 0 -1 6 0 0 -1 0 0 0 0 0 -1 0 0 0 0 0 0 0 0 0 -1 0 0 0 0 0 -1 0 0 6 -1 0 0 0 0 0 0 0 -1 0 0 0 0 0 0 0 0 0 -1 0 0 0 0 0 -1 0 -1 6 -1 0 0 0 0 0 0 0 -1 0 0 0 0 0 0 0 0 0 -1 0 0 0 0 0 -1 0 -1 6 0 0 0 0 0 0 0 0 -1 0 0 0 0 0 0 0 0 0 -1 0 0 0 0 0 0 0 0 6 -1 0 -1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 -1 0 0 0 0 0 0 0 -1 6 -1 0 -1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 -1 0 0 0 0 0 0 0 -1 6 0 0 -1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 -1 0 0 0 0 0 -1 0 0 6 -1 0 -1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 -1 0 0 0 0 0 -1 0 -1 6 -1 0 -1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 -1 0 0 0 0 0 -1 0 -1 6 0 0 -1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 -1 0 0 0 0 0 -1 0 0 6 -1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 -1 0 0 0 0 0 -1 0 -1 6 -1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 -1 0 0 0 0 0 -1 0 -1 6