3
1. . ,
,
(), . , , .
(i =1,2,, n)
, .
A =
1.
l4 p1 l3 p2 l2 p3 l p4 = 0
:
0 ¾ ; 1 = 0; 2 = 1; 3 = 2; 4 = 3.
0, 1, 2, 3 , p1, p2, p3, p4 ,
4 = p1 3 + p2 2 + p3 1 + p4 0.
Excel MathCAD, 1.
1
0 | 1 | 2 | 3 | 4 | ||||
2,2 | 0,5 | 2,2 | 10,09 | 52,373 | 291,0006 | |||
1,3 | 6,5 | 41,84 | 239,605 | |||||
0,5 | 0,5 | 1,6 | 0,5 | 6,55 | 37,64 | 220,7825 | ||
1,6 | 10,20 | 57,56 | 321,930 |
,
. (*)
2. (*), , Excel MathCAD, 2.
:
l1 = 5,652; l2 = 1,545; l3 = 1,420; l4 = 0,2226.
3. X i, l i,
X i= b i 3B0 + b i 2B1 + b i 1B2 + b i 0B3,
0, 1, 2, 3
= b i 0l3 + b i 1l2 + b i 2 + b i 3.
, . , , , .
2.
2
l i | b i 3B0 | b i 2B1 | b i 1B2 | b i 0B3 | X i | |
5,652 | 0,4877 | 4,7672 2,1669 1,0334 4,3338 | 3,5113 2,2620 2,2794 3,5496 | 52,373 41,84 37,64 57,56 | 44,5822 37,4111 34,2772 49,6766 | 0,879 0,753 0,690 1,0 |
1,545 | 1,7918 | 15,5826 7,08298 3,5415 14,1660 | 44,9510 28,9575 29,1802 45,4410 | 52,373 41,84 37,64 57,56 | 6,3688 5,7995 4,9183 2,0470 | 0,911 0,772 0,321 |
1,420 | 1,9427 | 22,7400 10,3364 5,1682 20,6728 | 74,8678 48,2300 48,6010 75,6840 | 52,373 41,84 37,64 57,56 | 1,6975 3,9464 5,7928 2,5488 | 0,293 0,681 0,440 |
0,2226 | 12,4042 | 5,2692 1,4860 0,7430 2,9720 | 58,2940 37,5531 37,8420 58,9295 | 52,373 41,84 37,64 57,56 | 3,2140 2,8009 0,9450 4,3415 | 0,740 0,645 0,218 |
|
|
2. . A n-1
P=
:
( );
A =
1. , . :
= -11× -12× -13×3×2×1.
,
l4 6l3 0,2l2 + 12,735l 2,7616 = 0.
Excel MathCAD, 2. :
l1 = 5,652; l2 = 1,545; l3 = 1,420; l4 = 0,2226.
2. X i, l i,
X i = 3 ×2× 1×Y i, Y i = .
3.
3
li | M1 | M2 | M3 | Yi | Xi | |
5,652 | 0,231125 1,078582 1,651001 1,158706 | 0,351515 0,242424 1,060606 0,681212 | 1,25 0,625 0,625 1,25 | 180,5537 31,9451 5,652 | 0,8977 0,7529 0,6898 | 0,898 0,753 0,690 |
1,545 | 0,231125 1,078582 1,651001 1,158706 | 0,351515 0,242424 1,060606 0,681212 | 1,25 0,625 0,625 1,25 | 3,6880 2,3870 1,545 | 3,1143 2,8359 2,4048 | 0,911 0,772 0,440 |
0,2226 | 0,231125 1,078582 1,651001 1,158706 | 0,351515 0,242424 1,060606 0,681212 | 1,25 0,625 0,625 1,25 | 0,01103 0,4955 0,2226 | 0,7403 0,6451 0,2177 | 0,740 0,645 0,218 |
1,420 | 0,231125 1,078582 1,651001 1,158706 | 0,351515 0,242424 1,060606 0,681212 | 1,25 0,625 0,625 1,25 | 2,8633 2,0164 1,420 | 0,6665 1,5480 2,2719 | 0,293 0,681 0,440 |
3. . : , .
;
.
1. , - ; , .
4.
4
1,6 | 2,3 | 1,2 | ||||
A | 2,3 | 0,6 | 1,5 | |||
1,2 | 1,5 | 3,8 | ||||
5,1 | 4,4 | 6,5 | 5,11 | 5,48 | 5,76 | |
26,08 | 24,12 | 37,42 | 5,45 | 5,41 | 5,60 | |
142,108 | 130,586 | 209,672 | 5,484 | 5,511 | 5,548 | |
5,5151 | 5,5148 | 5,5321 | ||||
5,5205 | 5,5225 | 5,5267 | ||||
5,5233 | 5,5235 | 5,5251 | ||||
5,5240 | 5,5241 | 5,5246 | ||||
5,5242 | 5,5243 | 5,5244 | ||||
5,5243 | 5,5243 | 5,5244 | ||||
5,5243 | 5,5243 | 5,5243 | ||||
, .
|
|
2. . , . , , , . . .
3
:
1. . MathCAD Mathematica ( ). VBA ( Excel).
2. , ( ). , , 1. .
3. , .
:
1. . MathCAD Mathematica ( ). VBA ( Excel).
2. , ( ). , , 1. .
3. , .
1. A = 2. =
3. A = 4. =
5. A = 6. =
7. A = 8. =
9. A = 10. =
11. A = 12. =
13. A = 14. =
15. A = 16. =
17. A = 18. =
19. A = 20. =
21. A = 22. =
23. A = 24. =
25. A = 26. =
27. A = 28. =
29. A = 30. =