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ɐɟɣ ɿɧɬɟɝɪɚɥ ɡɜɨɞɢɬɶɫɹ ɞɨ ɩɨɜɬɨɪɧɨɝɨ, ɹɤɳɨ ɜɜɟɫɬɢ |
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Ⱦɨ ɨɞɧɨɤɪɚɬɧɢɯ ɿɧɬɟɝɪɚɥɿɜ ɦɨɠɧɚ ɡɚɫɬɨɫɭɜɚɬɢ ɤɜɚɞɪɚɬɭɪɧɭ ɮɨɪɦɭɥɭ |
ɫɟɪɟɞɧɿɯ ɩɪɹɦɨɤɭɬɧɢɤɿɜ. Ɍɨɞɿ |
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Ʉɭɛɚɬɭɪɧɚ ɮɨɪɦɭɥɚ (ɰɟ ɮɨɪɦɭɥɚ ɧɚɛɥɢɠɟɧɨɝɨ ɨɛɱɢɫɥɟɧɧɹ ɿɧɬɟɝɪɚɥɭ (1)), |
ɹɤɳɨ ɜɢɤɨɪɢɫɬɨɜɭɽɬɶɫɹ ɮɨɪɦɭɥɚ ɬɪɚɩɟɰɿʀ ɦɚɽ ɜɢɝɥɹɞ: |
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a)(d |
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[ f (a,c) f (b,c) |
f (a,d) f (b,a)]. |
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Ɍɨɱɧɿɫɬɶ |
ɡɚɥɟɠɢɬɶ |
ɜɿɞ |
ɩɨɜɟɞɿɧɤɢ ɮɭɧɤɰɿʀ |
ɬɚ ɜɿɞ ɞɨɜɠɢɧɢ ɿɧɬɟɪɜɚɥɿɜ |
[a,b], [c,d]. ɧɚɥɨɝ ɮɨɪɦɭɥ ɫɤɥɚɞɟɧɨɝɨ ɬɢɩɭ ɞɥɹ (1) ɛɭɞɭɽɬɶɫɹ ɬɚɤɢɦ ɱɢɧɨɦ: ɪɨɡɛɢɜɚɽɦɨ D ɧɚ ɤɨɦɿɪɤɢ (ɞɢɜ. ɦɚɥɸɧɨɤ):
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{xi 1 d x d xi , y j 1 |
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y y j}, xi |
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Ɍɨɞɿ ɞɥɹ ɤɨɠɧɨɝɨ ɿɧɬɟɝɪɚɥɭ ɩɨ ɤɨɦɿɪɰɿ ɡɚɫɬɨɫɨɜɭɽɦɨ ɤɭɛɚɬɭɪɧɭ ɮɨɪɦɭɥɭ
ɩɪɹɦɨɤɭɬɧɢɤɿɜ (4): |
¦x ¦ |
³³ f (x, y)dxdy I0,h |
¦x ¦hxhy f (xi , yi ) |
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f (x, y) C2 ( |
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O(hx2 hy2 ). ɋɬɟɩɿɧɶ ɬɨɱɧɨɫɬɿ ɩɨ ɤɪɨɤɚɦ |
D |
I0,h |
2. ɋɤɥɚɞɧɿɫɬɶ ɦɟɬɨɞɭ ɩɪɨɩɨɪɰɿɣɧɚ ɤɿɥɶɤɨɫɬɿ ɤɨɦɿɪɨɤ
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O(N 2 ), |
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Ny . ȼ 3-ɜɢɦɿɪɧɨɦɭ ɩɪɨɫɬɨɪɿ f |
f (x, y, z) ɫɤɥɚɞɧɿɫɬɶ - Q O(N 3). |
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əɤɳɨ D ɧɟ ɩɪɹɦɨɤɭɬɧɢɤ, ɬɨ ɡɚɦɿɫɬɶ f |
ɜɜɟɞɟɦɨ |
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(x, y), |
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ɞɟ ɉ – ɧɚɣɦɟɧɲɢɣ ɨɯɨɩɥɸɸɱɢɣ D ɩɪɹɦɨɤɭɬɧɢɤ D |
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³³ f |
(x, y)dxdy , ɳɨ ɪɨɡɝɥɹɞɚɜɫɹ ɜɢɳɟ. |
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ɉ |
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ɇɟɞɨɥɿɤ ɬɚɤɨɝɨ ɩɿɞɯɨɞɭ: |
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(x, y) ɦɨɠɟ ɛɭɬɢ ɪɨɡɪɢɜɧɨɸ |
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ɮɭɧɤɰɿɽɸ ɿ ɱɟɪɟɡ ɰɟ ɧɢɡɶɤɚ ɬɨɱɧɿɫɬɶ ɨɛɱɢɫɥɟɧɧɹ |
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ɿɧɬɟɝɪɚɥɭ. |
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ɇɚɫɬɭɩɧɢɣ ɩɿɞɯɿɞ ɛɚɡɭɽɬɶɫɹ ɧɚ ɜɿɞɩɨɜɿɞɧɿɣ ɡɚɦɿɧɿ ɡɦɿɧɧɢɯ |
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f (x([,K), y([,K))J([,K)d[dK, |
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y y( , ) |
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ɩɪɹɦɨɤɭɬɧɢɤ ɜ ɩɥɨɳɢɧɿ |
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J( |
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əɤɳɨ |
ɝɪɚɧɢɰɹ ɨɛɥɚɫɬɿ D ɝɥɚɞɤɚ, ɬɨ ɹɤɨɛɿɚɧ ɛɭɞɟ ɦɚɬɢ ɨɫɨɛɥɢɜɨɫɬɿ, ɳɨ ɬɚɤɨɠ ɡɧɢɠɭɽ ɲɜɢɞɤɿɫɬɶ ɡɛɿɠɧɨɫɬɿ.
ɓɟ ɨɞɢɧ ɩɿɞɯɿɞ ɜ ɨɛɱɢɫɥɟɧɧɿ ɿɧɬɟɝɪɚɥɭ ɩɨ ɞɨɜɿɥɶɧɿɣ ɨɛɥɚɫɬɿ D ɛɚɡɭɽɬɶɫɹ ɧɚ ɬɪɢɚɧɝɭɥɸɜɚɧɧɹ ɨɛɥɚɫɬɿ. əɤɳɨ ɨɛɥɚɫɬɶ ɞɨɜɿɥɶɧɨɝɨ ɜɢɝɥɹɞɭ, ɬɨ ʀʀ ɦɨɠɧɚ
N
ɪɨɡɛɢɬɢ ɧɚ ɬɪɢɤɭɬɧɢɤɢ ɬɚɤɢɦ ɱɢɧɨɦ D Dk :
k 1
N |
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³³ f (x, y)dxdy. Ɂɚɫɬɨɫɭɽɦɨ ɤɭɛɚɬɭɪɧɿ ɮɨɪɦɭɥɢ ɞɨ |
Ɍɨɞɿ I ¦Ik , Ik |
k |
1 |
Dk |
ɤɨɠɧɨɝɨ Ik |
Ikh . Ⱦɥɹ ɰɶɨɝɨ ɡɚɦɿɧɢɦɨ ɮɭɧɤɰɿɸ ɩɨɥɿɧɨɦɨɦ ɩɟɪɲɨɝɨ ɫɬɟɩɟɧɹ |
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f (x, y) L1(x, y) A Bx Cy . |
Ɂɚɞɚɱɚ 35 ɉɨɛɭɞɭɜɚɬɢ ɹɜɧɢɣ ɜɢɝɥɹɞ ɤɭɛɚɬɭɪɧɨʀ ɮɨɪɦɭɥɢ, ɹɤɚ ɞɨɡɜɨɥɹɽ ɧɚɛɥɢɠɟɧɨ ɨɛɱɢɫɥɢɬɢ Ik ɩɨ ɬɪɢɤɭɬɧɢɤɭ Dk , ɹɤɳɨ ɡɚɦɿɧɢɬɢ f (x, y) L1(x, y)
ɧɚ ɿɧɬɟɪɩɨɥɹɰɿɣɧɢɣ ɛɚɝɚɬɨɱɥɟɧ 1-ɝɨ ɫɬɟɩɟɧɹ.
Ɍɨɱɧɿɫɬɶ ɬɚɤɨɝɨ ɩɿɞɯɨɞɭ
I I h I ¦N Ikh O(h2 ),
k 1
ɞɟ h maxdiamDk .
k
102
ɋɤɥɚɞɧɿɫɬɶ ɨɛɱɢɫɥɟɧɧɹ ɿɧɬɟɝɪɚɥɚ: Q O(h 2 ) ɞɥɹ D R2 ; Q O(h 3) ɞɥɹ
D R3. |
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Ɇɨɠɧɚ ɡɝɭɫɬɢɬɢ ɫɿɬɤɭ, |
ɩɨɞɿɥɢɜɲɢ ɨɞɢɧ ɬɪɢɤɭɬɧɢɤ |
Dk ɧɚ ɱɨɬɢɪɢ (ɞɢɜ. |
ɦɚɥɸɧɨɤ): |
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ȱ, ɧɚɪɟɲɬɿ, ɪɨɡɝɥɹɧɟɦɨ ɿɞɟɸ ɦɟɬɨɞɭ ɫɬɚɬɢɫɬɢɱɧɢɯ ɜɢɩɪɨɛɭɜɚɧɶ (ɦɟɬɨɞ |
Ɇɨɧɬɟ-Ʉɚɪɥɨ) ɞɥɹ |
ɨɛɱɢɫɥɟɧɧɹ |
ɿɧɬɟɝɪɚɥɭ |
I |
³³ f (x, y)dxdy. |
Ɂɚɦɿɧɢɦɨ |
ɧɚɛɥɢɠɟɧɨ |
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³³ f |
(x, y)dxdy |
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ɉ – ɧɚɣɦɟɧɲɢɣ ɨɯɨɩɥɸɸɱɢɣ D ɩɪɹɦɨɤɭɬɧɢɤ |
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ɩɪɨɞɨɜɠɟɧɧɹ ɮɭɧɤɰɿʀ (4); i , |
i - ɧɟɡɚɥɟɠɧɿ ɪɟɚɥɿɡɚɰɿʀ ɪɿɜɧɨɦɿɪɧɨ ɪɨɡɩɨɞɿɥɟɧɢɯ |
ɧɚ |
[a,b] ɬɚ [c,d] ɜɢɩɚɞɤɨɜɢɯ ɜɟɥɢɱɢɧ |
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ɋɤɥɚɞɧɿɫɬɶ ɰɶɨɝɨ ɦɟɬɨɞɭ |
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O(N). Ɉɰɿɧɤɚ ɬɨɱɧɨɫɬɿ |
I IN |
O(N |
2 |
) ɧɨɫɢɬɶ ɣɦɨɜɿɪɧɢɫɬɧɢɣ ɯɚɪɚɤɬɟɪ. |
ɉɨɡɢɬɢɜɧɚ ɫɬɨɪɨɧɚ ɦɟɬɨɞɭ – ɧɟɡɚɥɟɠɧɚ ɜɿɞ ɪɨɡɦɿɪɧɨɫɬɿ ɫɤɥɚɞɧɿɫɬɶ; ɧɟɝɚɬɢɜɧɚ
– ɧɢɡɶɤɚ ɬɨɱɧɿɫɬɶ.
10. ɑɢɫɟɥɶɧɿ ɦɟɬɨɞɢ ɪɨɡɜ’ɹɡɚɧɧɹ ɡɚɞɚɱɿ Ʉɨɲɿ ɞɥɹ ɡɜɢɱɚɣɧɢɯ ɞɢɮɟɪɟɧɰɿɣɧɢɯ ɪɿɜɧɹɧɶ
ɉɨɫɬɚɧɨɜɤɚ ɡɚɞɚɱɿ : ɧɟɯɚɣ ɩɨɬɪɿɛɧɨ ɡɧɚɣɬɢ ɪɨɡɜ’ɹɡɨɤ ɞɢɮɟɪɟɧɰɿɣɧɨɝɨ
ɪɿɜɧɹɧɧɹ ɡ ɩɨɱɚɬɤɨɜɢɦɢ ɭɦɨɜɚɦɢ
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əɤɳɨ ɞɨɜɿɥɶɧɚ ɮɭɧɤɰɿɹ |
fk ɧɟɩɟɪɟɪɜɧɚ ɩɨ ɤɨɠɧɿɣ ɫɜɨʀɣ ɡɦɿɧɧɿɣ ɬɚ ɩɨ u j ɜɨɧɢ |
Ʌɿɩɲɢɰɶ-ɧɟɩɟɪɟɪɜɧɿ, ɬɨɛɬɨ |
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ɬɨ ɪɨɡɜ’ɹɡɨɤ ɡɚɞɚɱɿ (1) ɿɫɧɭɽ ɿ ɽɞɢɧɢɣ.
ɇɟɯɚɣ ɡɚɞɚɧɨ ɪɿɜɧɹɧɧɹ m-ɨɝɨ ɩɨɪɹɞɤɭ ɬɚ ɩɨɱɚɬɤɨɜɿ ɭɦɨɜɢ: |
° |
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F(t,v,v ,...,v(m 1) ), |
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t0 :v |
v2,...,v(m 1) vm. |
ȼɜɟɞɟɦɨ ɤɨɦɩɨɧɟɧɬɢ ɜɟɤɬɨɪɚ u : uk (t) |
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1) (t) . Ɍɨɞɿ ɡɚɞɚɱɚ (2) ɡɚɩɢɫɭɽɬɶɫɹ |
ɭ ɜɢɝɥɹɞɿ ɫɢɫɬɟɦɢ (1): |
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Ɍɨɦɭ ɞɚɥɿ, ɜ ɨɫɧɨɜɧɨɦɭ, ɪɨɡɝɥɹɞɚɸɬɶɫɹ ɦɟɬɨɞɢ ɪɨɡɜ‘ɹɡɚɧɧɹ ɡɚɞɚɱɿ (1).
10.1. ɇɚɛɥɢɠɟɧɿ ɚɧɚɥɿɬɢɱɧɿ ɦɟɬɨɞɢ [ȻɀɄ 358-360; ɅɆɋ 254-255] 1) Ɇɟɬɨɞ ɩɨɫɥɿɞɨɜɧɢɯ ɧɚɛɥɢɠɟɧɶ (ɦɟɬɨɞ ɉɿɤɚɪɚ)
ɉɨɬɪɿɛɧɨ ɪɨɡɜ’ɹɡɚɬɢ ɞɢɮɟɪɟɧɰɿɣɧɟ ɪɿɜɧɹɧɧɹ ɡ ɜɿɞɩɨɜɿɞɧɢɦɢ ɩɨɱɚɬɤɨ- ɜɢɦɢ ɭɦɨɜɚɦɢ:
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du |
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u0 . |
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(1) |
ɉɪɨɿɧɬɟɝɪɭɽɦɨ (1) |
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dt |
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u(t0 ) ³t |
f ([,u([))d[ |
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u(t) |
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(2) |
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t0 |
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Ɂɚɞɚɽɦɨ u(0) (t) ɿ ɡɚɩɢɲɟɦɨ ɿɬɟɪɚɰɿɣɧɢɣ ɩɪɨɰɟɫ: |
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u(k 1) (t) |
u0 |
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³t |
f ([,u(k) ([))d[, k 0,1,.... |
(3) |
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t0 |
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ȱɫɧɭɽ T |
T(u0 , L) ( L |
maxLj - ɫɬɚɥɚ Ʌɿɩɲɢɰɹ) ɬɚɤɚ, ɳɨ |
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u(n) (t) o u(t), t [t0 ,T]. |
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nof |
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Ɍɨɦɭ u(t) |
u(n) (t). |
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ɇɟɞɨɥɿɤ ɦɟɬɨɞɭ: ɧɟɨɛɯɿɞɧɨ ɩɪɨɜɟɞɟɧɧɹ ɚɧɚɥɿɬɢɱɧɨɝɨ ɿɧɬɟɝɪɭɜɚɧɧɹ |
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2) Ɇɟɬɨɞ ɪɹɞɿɜ Ɍɟɣɥɨɪɚ |
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ɇɟɯɚɣ ɪɨɡɜ’ɹɡɨɤ ɡɚɞɚɱɿ (1) ɦɨɠɧɚ ɩɪɟɞɫɬɚɜɢɬɢ ɭ ɜɢɝɥɹɞɿ ɪɹɞɭ |
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f |
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(k) |
(t0 ) |
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u(t) |
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(t t0 )k . |
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k 0 |
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k! |
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Ȼɭɞɟɦɨ ɲɭɤɚɬɢ ɧɚɛɥɢɠɟɧɧɹ ɭ ɜɢɝɥɹɞɿ ɫɤɿɧɱɟɧɨʀ ɫɭɦɢ |
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N |
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(k) |
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u(t) |
uN (t) |
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t0 )k , t [t0 ,t1]. |
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Ⱦɥɹ ɜɢɡɧɚɱɟɧɧɹ u k t0 |
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k! |
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ɞɢɮɟɪɟɧɰɿɸɽɦɨ ɪɿɜɧɹɧɧɹ (1) ɩɨ t : |
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u(0) (t |
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əɤɳɨ W |
u(2) (t0 ) |
ft,0 |
fu,0 f0 , |
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2 ftu,0 f0 fuu,0 f0 |
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t1 t0 ɦɚɥɢɣ ɩɚɪɚɦɟɬɪ, ɬɨ |
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104 |
u(t) uN (t) O(WN 1) .
ɇɟɞɨɥɿɤɢ ɦɟɬɨɞɭ:
–ɡɪɨɫɬɚɧɧɹ ɤɿɥɶɤɨɫɬɿ ɞɨɞɚɧɤɿɜ ɩɪɢ ɨɛɱɢɫɥɟɧɧɿ u(n) (t0 ) ;
–ɧɟɨɛɯɿɞɧɨ ɚɧɚɥɿɬɢɱɧɨɝɨ ɞɢɮɟɪɟɧɰɿɸɜɚɧɧɹ.
10.2.Ɇɟɬɨɞɢ ɬɢɩɭ ȿɣɥɟɪɚ [ɋȽ, 214218]
Ɋɨɡɝɥɹɧɟɦɨ ɡɚɞɚɱɭ Ʉɨɲɿ: |
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du |
f t,u , u t0 |
u0 . |
(1) |
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dt |
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ȼɢɤɨɪɢɫɬɚɽɦɨ ɩɟɪɲɟ ɧɚɛɥɢɠɟɧɧɹ ɡɚ ɞɨɩɨɦɨɝɨɸ ɪɹɞɿɜ Ɍɟɣɥɨɪɚ ɧɚ ɩɪɨɦɿɠɤɭ |
t0 d t d t1: |
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t t0 f t0 ,u0 . |
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u t u1 t u t0 |
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Ɉɛɱɢɫɥɢɦɨ ɧɚɛɥɢɠɟɧɟ ɡɧɚɱɟɧɧɹ ɜ ɬɨɱɰɿ t1: |
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ɞɟ W |
u t1 |
u1 |
u1 t1 |
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u0 Wf t0 ,u0 , |
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t1 t0 - ɞɟɹɤɢɣ ɤɪɨɤ. əɤɳɨ ɩɨɡɧɚɱɢɬɢ y1 |
u(t1), y0 |
u(t0 ), |
ɬɨ ɦɚɽɦɨ |
ɮɨɪɦɭɥɭ |
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f t0 , y0 . |
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Ɂɚɫɬɨɫɨɜɭɸɱɢ ɬɚɤɢɣ ɩɿɞɯɿɞ ɞɥɹ tn |
t |
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tn 1, ɨɬɪɢɦɚɽɦɨ ɪɟɤɭɪɟɧɬɧɭ ɮɨɪɦɭɥɭ |
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yn |
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u0 , |
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ɐɟ ɮɨɪɦɭɥɚ ɦɟɬɨɞɭ ȿɣɥɟɪɚ. Ʉɪɨɤ ɿɧɬɟɝɪɭɜɚɧɧɹ ɦɨɠɟ ɡɦɿɧɸɜɚɬɢɫɹ:
ntn 1 tn .
Ƚɟɨɦɟɬɪɢɱɧɚ ɿɧɬɟɪɩɪɟɬɚɰɿɹ ɦɟɬɨɞɭ ȿɣɥɟɪɚ ɩɪɟɞɫɬɚɜɥɟɧɚ ɧɚ ɪɢɫ.1. Ƀɨɝɨ ɞɪɭɝɚ ɧɚɡɜɚ – ɦɟɬɨɞ ɥɚɦɚɧɢɯ.
y3
u(t)
y2
y1 y0
Ɋɢɫ. 1 ɐɟɣ ɦɟɬɨɞ ɜɿɞɧɨɫɢɬɶɫɹ ɞɨ ɨɞɧɨɤɪɨɤɨɜɢɯ, ɬɨɛɬɨ ɪɨɡɜ’ɹɡɨɤ ɧɚ ɧɚɫɬɭɩɧɨɦɭ
ɤɪɨɰɿ ɨɛɱɢɫɥɸɽɬɶɫɹ ɬɿɥɶɤɢ ɩɨ ɨɞɧɨɦɭ ɡɧɚɱɟɧɧɸ ɧɚ ɩɨɩɟɪɟɞɧɶɨɦɭ ɤɪɨɰɿ.
Ɂɚɝɚɥɶɧɚ ɮɨɪɦɭɥɚ ɨɞɧɨɤɪɨɤɨɜɢɯ ɦɟɬɨɞɿɜ |
, yn , f |
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yn ) tn |
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Wf tn , yn |
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Ⱦɥɹ ɦɟɬɨɞɭ ȿɣɥɟɪɚ ) |
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22
Ɍɚɤɢɦ ɱɢɧɨɦ ɦɟɬɨɞ ɬɪɚɩɟɰɿɣ ɦɚɽ ɞɪɭɝɢɣ ɩɨɪɹɞɨɤ ɚɩɪɨɤɫɢɦɚɰɿʀ.
Ɂɚɞɚɱɚ 36 ɉɨɤɚɡɚɬɢW , ɳɨ ɩɨɯɢɛɤɚ ɧɚ ɨɞɧɨɦɭ ɤɪɨɰɿ ɦɟɬɨɞɭ ɬɪɚɩɟɰɿɣ ɽ ɜɟɥɢɱɢɧɚ ɩɨɪɹɞɤɭ O 3 .
Ɍɚɤɢɦ ɱɢɧɨɦ ɦɢ ɨɬɪɢɦɚɥɢ ɛɿɥɶɲ ɬɨɱɧɢɣ ɦɟɬɨɞ. ɇɟɞɨɥɿɤ ɦɟɬɨɞɭ
ɬɪɚɩɟɰɿɣ |
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ɧɟɹɜɧɿɫɬɶ (ɬɪɟɛɚ ɪɨɡɜ’ɹɡɭɜɚɬɢ |
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ɧɟɥɿɧɿɣɧɟ ɪɿɜɧɹɧɧɹ). Ⱦɥɹ |
ɪɨɡɜ’ɹɡɚɧɧɹ |
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ɧɟɹɜɧɨɫɬɿ |
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ɡɚɫɬɨɫɭɽɦɨ |
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ɦɟɬɨɞ |
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ɩɪɟɞɢɤɬɨɪ-ɤɨɪɪɟɤɬɨɪ |
(ɩɪɟɞɢɤɬɨɪ - ɩɨɩɟɪɟɞɧɢɤ, ɤɨɪɟɤɬɨɪ - ɭɬɨɱɧɸɜɚɱ). |
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Ɉɛɱɢɫɥɢɦɨ ɩɨɩɟɪɟɞɧɶɨ ɡɚ ɹɜɧɢɦ ɦɟɬɨɞɨɦ ȿɣɥɟɪɚ |
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n 1 |
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ɍɬɨɱɧɢɦɨ ɡɚ ɦɟɬɨɞɨɦ ɬɪɚɩɟɰɿɣ |
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f tn 1, |
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yn 1 |
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Ɏɨɪɦɭɥɢ (7) ɬɚ (8) ɭɬɜɨɪɸɸɬɶ ɦɟɬɨɞ ȿɣɥɟɪɚ-Ʉɨɲɿ. |
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Ɉɰɿɧɢɦɨ ɩɨɯɢɛɤɭ ɧɚ ɨɞɧɨɦɭ ɤɪɨɰɿ: |
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R(W) y1 |
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f (t0 W,u0 Wf (t0 , y0 )@ u(t0 W) , |
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0. Ⱦɚɥɿ |
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Rc( ) |
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du (t0 ) |
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ɓɟ ɨɞɢɧ ɦɟɬɨɞ ɰɶɨɝɨ ɬɢɩɭ: |
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ɐɟ ɦɨɞɢɮɿɤɨɜɚɧɢɣ ɦɟɬɨɞ ȿɣɥɟɪɚ. ɇɚ ɟɬɚɩɿ ɤɨɪɟɤɬɨɪ (11) ɜɢɤɨɪɢɫɬɨɜɭɽɦɨ ɮɨɪɦɭɥɭ ɫɟɪɟɞɧɿɯ ɩɪɹɦɨɤɭɬɧɢɤɿɜ, ɚ ɩɪɟɞɢɤɬɨɪ – ɰɟ ɦɟɬɨɞ ȿɣɥɟɪɚ ɧɚ ɿɧɬɟɪɜɚɥɿ
(tn ,tn 1 ). W W
2
Ɂɚɞɚɱɚ 37 ɉɨɤɚɡɚɬɢ, ɳɨ ɞɥɹ ɦɨɞɢɮɿɤɨɜɚɧɨɝɨ ɦɟɬɨɞɭ ȿɣɥɟɪɚ R O 3 , ɬɨɛɬɨ m 2.
10.3. Ɇɟɬɨɞɢ ɬɢɩɭ Ɋɭɧɝɟ-Ʉɭɬɬɚ [ɋȽ, 218-221], [ɅɆɋ, 256-261]
Ɇɟɬɨɞɢ ɬɢɩɭ ȿɣɥɟɪɚ ɦɚɸɬɶ ɧɢɡɶɤɭ ɬɨɱɧɿɫɬɶ (m 1,2 ). Ɋɭɧɝɟ ɡɚɩɪɨɩɨɧɭɜɚɜ
ɦɟɬɨɞ ɬɪɟɬɶɨɝɨ, ɚ Ʉɭɬɬɚ ɪɨɡɜɢɧɭɜ ɣɨɝɨ ɿɞɟɸ ɬɚ ɨɬɪɢɦɚɜ ɦɟɬɨɞɢ ɱɟɬɜɟɪɬɨɝɨ ɩɨɪɹɞɤɭ ɬɨɱɧɨɫɬɿ.
Ɋɨɡɝɥɹɧɟɦɨ ɡɚɞɚɱɭ Ʉɨɲɿ |
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əɜɧɢɣ m- ɟɬɚɩɧɢɣ (ɫɬɚɞɿɣɧɢɣ) ɦɟɬɨɞ Ɋɭɧɝɟ-Ʉɭɬɬɚ ɩɨɥɹɝɚɽ ɜ ɧɚɫɬɭɩɧɨɦɭ. |
ɇɟɯɚɣ ɪɨɡɜ’ɹɡɨɤ |
yn |
y tn |
ɜɠɟ ɜɿɞɨɦɢɣ. Ɂɚɞɚɸɬɶɫɹ ɱɢɫɥɨɜɿ ɤɨɟɮɿɰɿɽɧɬɢ i , |
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ɿ ɩɨɫɥɿɞɨɜɧɨ ɨɛɱɢɫɥɸɸɬɶɫɹ ɡɚ ɮɨɪɦɭɥɚɦɢ: |
2,m |
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1 ɬɚ pi ,i |
1,m |
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m,m 1W km 1 . |
ɉɨɬɿɦ ɡ ɮɨɪɦɭɥɢ
ɡɧɚɯɨɞɢɦɨ ɧɨɜɟ ɡɧɚɱɟɧɧɹ yn 1
Ʉɨɟɮɿɰɿɽɧɬɢ Di , Eij , pi
ɞɥɹ ɬɨɝɨ, ɳɨɛ ɪɿɜɧɹɧɧɹ (2)
¦
m
pi 1.
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y tn 1 |
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ɜɢɛɢɪɚɽɦɨ ɡ ɦɿɪɤɭɜɚɧɶ ɬɨɱɧɨɫɬɿ. ɇɚɩɪɢɤɥɚɞ, ɚɩɪɨɤɫɢɦɭɜɚɥɨ ɪɿɜɧɹɧɧɹ (1), ɧɟɨɛɯɿɞɧɨ, ɳɨɛ
i 1
ȱɧɮɨɪɦɚɰɿɹ ɩɪɨ m- ɫɬɚɞɿɣɧɢɣD ɦɟɬɨɞ ɡɚɩɢɫɭɽɬɶɫɹ ɜ ɬɚɛɥɢɰɿ Ȼɚɬɱɟɪɚ:
D12 0E21
Dm Em1 |
Emm 1 |
p1 .... |
pm 1 pm |
ɉɨɯɢɛɤɚ ɧɚ ɨɞɧɨɦɭ ɤɪɨɰɿ
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Ⱦɥɹ ɬɨɝɨ, ɳɨɛ R W |
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,ɬɨɛɬɨ ɦɟɬɨɞ ɦɚɜ |
p -ɣ ɫɬɟɩɿɧɶ ɬɨɱɧɨɫɬɿ ɧɟɨɛɯɿɞɧɨ |
ɿ ɞɨɫɬɚɬɧɶɨ, ɳɨɛ R(0) |
Rc(0) ... R( p) (0) |
0 . Ɂɚɝɚɥɶɧɨɝɨ ɪɨɡɜ’ɹɡɤɭ ɰɿɽʀ |
ɧɟɥɿɧɿɣɧɨʀ ɫɢɫɬɟɦɢ ɧɟɦɚɽ, ɬɨɦɭ ɪɨɡɝɥɹɧɟɦɨ ɱɚɫɬɢɧɧɿ ɜɢɩɚɞɤɢ. |
u t0 |
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1. Ɇɟɬɨɞɢ ɩɟɪɲɨɝɨ ɩɨɪɹɞɤɭ m 1. ɇɟɜɿɞɨɦɟ p1. |
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0. Ɍɨɦɭ R W |
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2. Ɇɟɬɨɞɢ ɞɪɭɝɨɝɨ ɩɨɪɹɞɤɭ m |
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2. Ɍɭɬ ɨɬɪɢɦɭɽɦɨ ɫɿɦɟɣɫɬɜɨ ɦɟɬɨɞɿɜ. |
ɇɟɜɿɞɨɦɿ |
p1, p2 ,D2 ,E21 . ȼɨɧɢ |
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ɿ ɨɞɢɧ ɩɚɪɚɦɟɬɪ ɡɚɥɢɲɚɽɬɶɫɹ ɜɿɥɶɧɢɦ. Ⱦɚɥɿ ɨɞɢɧ ɩɚɪɚɦɟɬɪ |
p1 |
ɮɿɤɫɭɽɦɨ ɿ |
ɨɬɪɢɦɭɽɦɨ ɤɨɧɤɪɟɬɧɢɣ ɦɟɬɨɞ. |
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– ɦɨɞɢɮɿɤɨɜɚɧɢɣ ɦɟɬɨɞ ȿɣɥɟɪɚ |
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1 – ɦɟɬɨɞ ȿɣɥɟɪɚ-Ʉɨɲɿ |
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Ɂɚɩɢɲɟɦɨ ɪɟɡɭɥɶɬɚɬ ɜɢɛɨɪɭ ɩɚɪɚɦɟɬɪɿɜ ɭ ɜɢɝɥɹɞɿ ɬɚɛɥɢɰɿ Ȼɚɬɱɟɪɚ (ɨɞɢɧ ɡ ɱɚɫɬɢɧɧɢɯ ɜɢɩɚɞɤɿɜ):
0
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