. , . , . , , , .
M = | mij | k × n. k ─ , . mij , ui , j. . , G (. 16.19) .
a | b | c | d | e | f | |||
1 | b | a | a | c | b | a | ||
= | 2 | c | c | b | e | c | b | |
3 | f | e | d | d | c | . | ||
4 | f | e | ||||||
5 | f |
.
. 16.19. G
. , .
1.1. a. G, a ( a ), b.
1.2. b:
= [ a ─ b ], b M.
1.3. , .
2.1. G, b, a, . . c.
2.2. c:
= [ a ─ b ─ c ], c M.
2.3. , .
3.1. G, c, a b , . d.
3.2. d:
= [ a ─ b ─ c ─ d ], d M.
3.3. , .
4.1. G, d, c e.
4.2. e:
= [ a ─ b ─ c ─ d ─ e ], e M.
4.3. , .
5.1. G, e, .
5.2. : = [ a ─ b - c ─ d ].
6.1. G, d, .
6.2. : = [ a ─ b ─ c ].
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7.1. G, c, d e.
7.2. e:
= [ a ─ b ─ c ─ e ], e M.
7.3. , .
8.1. G, e, b c, d.
8.2. d:
= [ a ─ b ─ c ─ e ─ d ], d M.
8.3. , .
9.1. G, d, .
9.2. : = [ a ─ b ─ c ─ e ].
10.1. G, e, .
10.2. : = [ a ─ b ─ c ].
11.1. G, c, e f.
11.2. f:
= [ a ─ b ─ c ─ f ], f M.
11.3. , .
12.1. G, f, .
12.2. : = [ a - b - c ].
13.1. G, c, .
13.2. : = [ a - b ].
14.1. G, b, c e.
14.2. e:
= [ a ─ b ─ e ], c M.
14.3. , .
15.1. G, e, b c.
15.2. c:
= [ a ─ b ─ e ─ c ], c M.
15.3. , .
16.1. G, c, d.
16.2. d:
= [ a ─ b ─ e ─ c ─ d ], d M.
16.3. , .
17.1. G, d, .
17.2. : = [ a ─ b ─ e ─ c ].
18.1. G, c, f.
18.2. f:
= [ a ─ b ─ e ─ c ─ f ], f M.
18.3. , .
19.1. G, f, .
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19.2. : = [ a ─ b ─ e ─ c ].
20.1. G, c, .
20.2. : = [ a ─ b ─ e ].
21.1. G, e, c d.
21.2. d:
= [ a ─ b ─ e ─ d ], c M.
21.3. , .
22.1. G, d, c.
22.2. c:
= [ a ─ b ─ e ─ d ─ c ], c M.
22.3. , .
23.1. G, c, f.
23.2. f:
= [ a ─ b ─ e ─ d ─ c ─ f ], c M.
23.3. , .
24.1. G, f, a, .
23.2. a:
= [ a ─ b ─ e ─ d ─ c ─ f ─ a ].
23.3. , .
─ , . , , .
, . , .
. B PL. B = || bij ||, , xi xj , xj. PL = || pL ( i , j )|| B, pL ( i , j ) l. x 2 ´ x 3 ´¼ ´ xk -1, x 1 xk, x 1, x 2, x 3, ¼, xk -1, xk.
PL+1 = B ´ PL PL+1 = úç p L+1( s , t )úç, p L+1( s , t ) = .
PL+1 , . , , , , . , PL+1, . n ─ 1 Pn-1 , u(xk ─ x 1) .
1. G = (, U), . 16.20. , ─ .
. 16.20.
: . :
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.
.
1.1. a : L = { }.
2.1. a , . b: L = { a, b }.
2.2. |L| = n. , . 3.1.
3.1. b, ─ a. L, b c. .
3.2. L . : L = { a, b, c }.
3.3. |L| = n. , . 4.1.
4.1. c ─ b. L, c d. .
4.2. d L . : L = { a, b, c, d }.
4.3. |L| = n. , . 5.1.
5.1. d . . d L = { a, b, c }. . 6.1.
6.1. c e. .
6.2. e L . : L = { a, b, c, e }.
6.3. |L| = n. , 7.1.
7.1. e . . e L = { a, b, c }. 8.
8.1. c . . c L = { a, b }. . 9.1.
9.1. b d. .
9.2. d L . : L = { a, b, d }.
9.3. |L| = n. , . 10.1.
10.1. d c. .
10.2. c L . : L = { a, b, d, c }.
10.3. |L| = n. , . 11.1.
11.1. c e. .
11.2. e L . : L = { a, b, d, c, e }.
11.3. |L| = n. . , G , , .
11.4. e a, , , G :
{ a ─ b ─ d ─ c ─ e ─ a }.
11.5. .
2. G = (X, U), . 16.21. .
. 16.21.
:
1. B P1 . P1 .
B = .
2. B P1, :
a | b | c | d | e | |||
P2= | a | b+c+e | e | e | b+e | b+c | . |
b | e | a+d+e | a+e | e | a+d | ||
c | e | a+e | a+e | e | a | ||
d | b+e | e | e | b+e | b | ||
e | b+c | a+d | a | b | a+b+c+d |
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|
P2 , , :
a | b | c | d | e | |||
P2= | a | 0 | e | e | b+e | b+c | . |
b | e | 0 | a+e | e | a+d | ||
c | e | a+e | 0 | e | a | ||
d | b+e | e | e | 0 | b | ||
e | b+c | a+d | a | b | 0 |
3. B P2, :
a | b | c | d | e | |||
P3= | a | be+ce+eb+ec | ca+ce+ea+ed | ba+be+ea | be+ce+eb | ba+bd+ca | . |
b | de+db+eb+ec | ae+de+ea+ed | ae+de+ea | ab+ae+eb | ab+ac+db | ||
c | eb+ec | ae+ea+ed | ae+ea | ab+ae | ab+ac | ||
d | be+eb+ec | ea+ed | ba+be+ea | be+eb | ba+bd | ||
e | be+ce+db+de | ae+ca+ce+de | ae+ba+be+de | ab+ae+be+ce | ab+ac+ba+bd+ca+db |
, , . , a , a. . P2 :
a | b | c | d | e | |||
P3= | a | 0 | ce+ed | be | be+ce+eb | bd | |
b | de+ec | 0 | ae+de+ea | ae | ac | ||
c | eb | ae+ea+ed | 0 | ab+ae | ab | . | |
d | be+eb+ec | ea | ba+be+ea | 0 | ba | ||
e | db | ca | ba | ab | 0 |
4. B P3, :
a | b | c | d | e | |||
P4 = | a | bde+bec+ceb+edb | cae+cea+ced+eca | bde+bae+bea+eba | bae+cab+cae+ceb+eab | bac+cab | . |
b | dbe+deb+dec+edb | ace+aed+dea+eca | abe+dba+dbe+dea+eba | abe+ace+aeb+eab | abd+dba | ||
c | edb | ace+eca+aed | abe+eba | abe+ace+aeb+eab | abd | ||
d | bde+edb+bec | eca | bae+bde+bea+eba | bae+eab | bac | ||
e | bde+bec+ceb+dbe+deb+ dec | ace+aed+cae+cea+ced | abe+bae+bde+bea+dba+ dbe+dea | abe+ace+aeb+bae+cab+ cae+ceb | abd+bac+cab+dba |
P4 :
a | b | c | d | e | |||
a | 0 | ced | bde | ceb | 0 | . | |
b | dec | 0 | dea | ace | 0 | ||
P4 = | c | edb | aed | 0 | abe+aeb+eab | abd | |
d | bec | eca | bae+ bea+ eba | 0 | bac | ||
e | 0 | 0 | dba | cab | 0 |
P4 . , . , a d a c e b d. , , . P4 G :
a c e d b.
, . , c e d b a d b a c e.
, , , , . , , , . , . , , .
1. ?
2. .
3. ─?
4. ?
5. .
6. ?
7. ?
8. ?
9. ?
10. ?