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0 |2 O4 o: M; k. ` S$ P牛顿法优化程序代码如下:
- e$ n! v# x7 bfunction [x,minf] = minNewton(f,x0,eps)
* w3 A" ~% I; k8 e$ L2 j) S0 B' `format long;2 Z, B9 f4 J/ L, x" T( x' h+ v6 e
if nargin == 24 N* o( U! b# f: j* U
eps = 1.0e-6;
G' d4 H0 l' Dend- i! D2 K! z$ N' M; O" Y) R
. t8 _( k# ?: v1 h7 D" edf = diff(f);
& G7 [! m5 p7 F0 Sd2f = diff(df);; e3 i* q. P1 X4 }3 e
k = 0; _' c/ _) n/ \' n
tol = 1;
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while tol>eps( G1 d5 r# \. f+ z5 ~4 Y8 j- k
dfx = subs(df,findsym(df),x0);: l$ H, G9 ^ k) ]) r* X3 t# m1 P- |
if diff(d2f) == 0* v* z+ Y7 G3 s
d2fx = double(d2f);7 s2 M& H! G& H% D4 P
else* H# Y) q1 w8 u% d% x
d2fx = subs(d2f,findsym(d2f),x0);. i0 f) H6 G+ N: }6 x- Q
end- K! m" Y1 j7 G4 c6 A
x1 = x0 - dfx/d2fx;3 F/ S5 O b1 G
k = k + 1;
( ] R# {+ v% P* s& S. q tol = abs(dfx);
: |3 B; C, @# R x0 = x1;( A7 g" A5 J+ L' v, U) b
end9 K* z% k4 [4 j* K
V' B- U. w3 w# d0 ?x = x1;
/ E0 m9 a8 J" }/ y) o, |$ [minf = subs(f,findsym(f),x);
. I- S/ j& D0 ^+ S& n$ L+ Bformat short;
4 f, P" A- v5 \1 Q* K复制代码( s1 k5 y, C5 r; z* m$ `+ O
; _( Y, F9 s/ Q; O主程序代码如下:
3 Q9 V/ L, q3 H9 [. T8 ?, Jsyms t
& N" T7 C. z8 L! e8 Lf=t^2-log(t)-5
5 A; w& C* D, W5 G$ G& Z6 \& z0 }4 ]x=minNewton(f,2)6 v: R( V+ T2 T, r
复制代码
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运行主程序后,得到的结果如下:& {' |8 _+ }8 `' i4 [( J
>> minNewton_ex: Y( u, K& \' n. z0 a* B
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f =
3 L, s1 ]% r& v' f D9 J8 h1 ?3 Q: I
: m2 F/ \% m5 J) \3 S* _9 Ft^2 - log(t) - 5+ F' E, X1 ]6 @' P- h
6 A Z5 P4 J; f. g4 J! a
; V* ~+ e: o0 g" X v0 Rx =
- s. ]' _1 Q% t% H$ @- I5 C
6 S9 g( C2 u9 d5 z7273770929600966997213123375563852928/102866654982368426957842812511776591376 o5 g/ I' C/ }: h% J: P4 E6 [9 g6 i
+ d. b6 Z# x5 j1 J; `( i
" R; w5 [0 s W, P# ]5 E3 w! nx的值怎么会是这样,不应该是一个小数吗? |
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