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6 a/ B7 h( x/ o: p6 e7 `) T牛顿法优化程序代码如下:
: `1 _0 ?4 X; _: B& V7 }( l9 N+ @0 }function [x,minf] = minNewton(f,x0,eps)/ O7 i9 g6 H3 C: |% e7 P. a l/ O
format long; j1 M9 s) ^0 y2 l5 t. r$ d5 u; v
if nargin == 2
& x! X) e! e: s2 \- j- n eps = 1.0e-6;
: Q: _* A4 Y' M. ^4 Yend
3 ]! |. K' o) u G
) y: r8 l9 S) }df = diff(f);
- A7 J w' h& q5 L* }d2f = diff(df);
1 j* ~3 t; ~% @9 X, }k = 0;" e- B" V* z: ^0 Q' b t: b
tol = 1;
. f1 l! E$ g; _. ^* m9 o8 V% g. f2 j( z: i/ Q
while tol>eps$ x5 J- w R# ?! A
dfx = subs(df,findsym(df),x0);) S) R f* Y' M
if diff(d2f) == 0
6 o' {- |8 p, w1 u1 l# }* N+ Y d2fx = double(d2f);$ n2 t* G* Z h( x: ^6 P% T
else
0 H: [9 W* R: g d2fx = subs(d2f,findsym(d2f),x0);* N- d8 Y3 L: T% V
end
4 D+ z* [; J; a% z9 B x1 = x0 - dfx/d2fx;
3 Y+ K6 j5 p9 w2 a k = k + 1;
% q8 |0 \- A9 o7 T tol = abs(dfx);: b+ Y( o1 C+ ]3 `5 f7 E J
x0 = x1;
! J% J$ D f( e% N1 F; s& @7 iend) _7 w' D6 P g3 Q
" W# A; `9 A0 H1 @4 Hx = x1;
* s0 {6 t$ ]3 @' M9 S& Bminf = subs(f,findsym(f),x);6 u5 K% {+ {6 H1 q( B
format short;
0 A ^9 r' w) \. ^/ Z! j复制代码8 G+ V! i( R5 W
' d, c' Y; j y v主程序代码如下:
+ L# u" p2 T+ |syms t7 y. b' i* n% G9 R9 o) l1 {' u; |
f=t^2-log(t)-5
! y3 Z4 |! b# X' s! ~' C5 F) jx=minNewton(f,2)
( r8 e& ^4 U; D8 @4 ^复制代码
. V h2 ?! i: A$ C/ v
* f3 w/ s5 @# B' K; b/ j& a; ~( k运行主程序后,得到的结果如下:
* R0 f8 N- [& s* E4 j>> minNewton_ex
! t$ H3 m+ |* ?, X# l8 j) K. n" Y6 L" p5 i
f =' O/ @$ y1 b: v
( p: @1 S: W2 ?" z
t^2 - log(t) - 5! N9 p! d! \! l3 R
) _" D0 I% [6 O* h4 O) r2 e
8 z1 x# b9 D5 a% i" O) [" u+ ex =( P- q. K3 G. D4 j$ f5 b1 I9 N
% ~; X. X2 Q- M+ G) d
7273770929600966997213123375563852928/10286665498236842695784281251177659137
, W& l- U: i* c/ `/ D3 w8 t. U* i
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1 M& t+ g8 o1 F/ kx的值怎么会是这样,不应该是一个小数吗? |
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