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x
; C, ~- }9 N S7 n牛顿法优化程序代码如下:
! h3 C, a" J4 p8 k( Zfunction [x,minf] = minNewton(f,x0,eps)
7 ]* c, w9 _8 O) p+ @- X% {' dformat long;) ]2 ?2 X! W! a# S2 N+ G5 W! D O; S8 V @
if nargin == 2
$ P2 J' E' r, W eps = 1.0e-6;: _( C) F! o# U5 i/ ?* o6 g' o
end" i0 \* I4 i, z- j" N# `
0 l6 {+ K7 p7 i: X$ i8 D/ |df = diff(f);2 L0 j# k% a5 y3 h5 i
d2f = diff(df);
' t& o* Q8 B$ wk = 0;
$ h6 d: U5 m& D; `tol = 1;3 \* ]$ I. e3 u: k# a& I3 { T
1 z+ s2 G% M+ K
while tol>eps1 S/ v: x- `& \$ E9 z
dfx = subs(df,findsym(df),x0);% Q" q* z M7 v4 E7 Q
if diff(d2f) == 0
6 e& H% ^' N' ?' T R- Q; V d2fx = double(d2f);
1 Z- b- s w8 ] else- Y: J4 t1 [& w! B3 ]
d2fx = subs(d2f,findsym(d2f),x0);
& C& H% `3 F; k5 G3 G* p1 Y end
( i/ g2 L# o, ] x1 = x0 - dfx/d2fx;
! ^7 }, s* z% V6 d% N+ T, v" e4 ~! ^ k = k + 1;' O# U' W4 P* b1 @" {" v
tol = abs(dfx);
2 V" l! C, T. Y; ^3 ] x0 = x1;
5 @+ O' {0 K8 b; nend
4 @6 U+ x/ D% K$ G$ z( w
" L' V" \$ a9 {. `x = x1;' V; ]. a* ]/ y+ s
minf = subs(f,findsym(f),x);
* n0 v) y9 D' \$ Wformat short;& z8 \- f3 d6 P0 z8 e+ ^
复制代码8 w% Q+ p6 t+ [0 j* C
6 l: q0 ?. B& Q/ ~1 ]
主程序代码如下:
; U# i- G) m. G6 ~/ Y; ?syms t
; K9 d3 M6 F- O8 `& df=t^2-log(t)-5/ A: H* C( h' D" u! D! `
x=minNewton(f,2)
3 H6 W" Y" I) z6 w/ `0 K9 a复制代码
4 O8 n* c! o0 m3 |
+ J4 o: f- U4 ?# I9 i- ~& o运行主程序后,得到的结果如下:" o7 w! L& K# T+ H- `
>> minNewton_ex
5 s5 m; o# h2 ?! m4 w! ^, b
, G: N Z o! j% j0 Mf =+ A! v: \: J& S4 z" E
( A4 v$ B& a& n8 r
t^2 - log(t) - 5) J8 @# Z3 [: D9 L
+ o/ B( A( |+ c. ~' F& l& Z
0 j& g1 v. _: l' U# \# Y$ }x =
9 h; t) t; Q; v/ M( a8 S; m
6 d3 d" e7 s" w* \ @0 K3 B7273770929600966997213123375563852928/10286665498236842695784281251177659137
* a7 F9 q$ W9 v% N* B! }- e A) ?5 x
! h* z! f7 a" @0 T- V, u3 g# b+ j1 V2 k; R2 R4 C5 z* z
x的值怎么会是这样,不应该是一个小数吗? |
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