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解方程的二分法 matlab 程序 （ x^3-3*x^2+6*x-1=0）
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. C8 w- P" ~3 c! {3 ^ |% Bisection.m
# Y* i' p& r, I R9 Cfunction[k,x,f_value]=Bisection(f,a,b,eps1,eps2,N)6 e. B) F" W' u) ] n
fprintf('k ,a ,b ,x, f\n')
' e. `" E7 E, q& S% Mfor k=1:N! r2 s6 U- s% }0 s- ]+ T& B% P
x=(a+b)/2;
* {5 r" C% d* g/ I f_value=f(x);
7 w- @. I' ?8 b5 z4 C+ d4 Z8 I5 x fprintf( '%3d, %10.9f, %10.9f, %10.9f,%10.9f,\n'...* ] o( n5 `: p3 n' s- O( ]4 N9 I
,k ,a ,b ,x, f_value)
' z; g, o, }. l. h: B; H if abs(f_value)< eps1||0.5*(b-a)<eps22 l' i9 K# e% @9 K- h7 \
return
. K- R% {2 c u3 A5 v% c+ Y else
8 o% c" I! m. ^% U if f(x)*f(a)<09 a; r! a4 B |4 J" i2 }( m4 Y
b=x;
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a=x;. k; f4 @' R! m8 z- A3 c
end
. Q4 ]- k5 n7 Y7 ~$ b if k== N7 C2 b5 { Y2 O( n& Z2 n' @
warning ('算法超出最大迭代数!')
3 m# w+ C( U9 ~0 S0 }7 @9 Z2 O7 c end
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% examlpe7.m) x# l6 }. m) d( _0 X
a=0; b=1;8 s! j) k! U0 j+ P
eps1=1e-4;eps2=1e-4;
7 L: m2 \* @9 G1 Y. K8 P N=300;" g$ C* o3 I! \: L/ Q' L
f=@ (x) (x^3-3*x^2+6*x-1);, n8 l8 B) J0 }2 H
Hfun=@Bisection;
/ [8 x6 t; _% a" p[k,x,f_value]= feval(Hfun, f,a,b,eps1,eps2,N);1 m. K" j) B4 T( [7 w% g# \) ]
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运行结果
4 i2 F% C9 Z6 Z( ]: s7 P>> examlpe7
8 a* ^: P c1 m. |6 B7 kk ,a ,b ,x, f
# x' c8 ]6 \8 e2 R$ o( p7 T! j6 C( E- L4 I 1, 0.000000000, 1.000000000, 0.500000000,1.375000000,6 D$ S3 `3 ~1 D9 m0 p2 l
2, 0.000000000, 0.500000000, 0.250000000,0.328125000,
1 [4 j4 `" {5 ~! p7 F: H& G 3, 0.000000000, 0.250000000, 0.125000000,-0.294921875,
+ ]( l! w' P# w( ?/ x. X" | 4, 0.125000000, 0.250000000, 0.187500000,0.026123047,) p2 O, {6 ^# b& ~0 x
5, 0.125000000, 0.187500000, 0.156250000,-0.131927490,
) v' b: r1 L0 z' w 6, 0.156250000, 0.187500000, 0.171875000,-0.052295685,$ l3 S7 l+ ~. y2 D* V
7, 0.171875000, 0.187500000, 0.179687500,-0.012936115,
/ ?5 Y* ?. d1 } 8, 0.179687500, 0.187500000, 0.183593750,0.006630838,) j) Q" l* r) O$ T! d: r
9, 0.179687500, 0.183593750, 0.181640625,-0.003143273,
+ W' w6 f! { s- i/ a 10, 0.181640625, 0.183593750, 0.182617188,0.001746121,6 A$ _: n* q- G6 W( {4 b5 [3 g% B. O6 l
11, 0.181640625, 0.182617188, 0.182128906,-0.000697991,' E3 |" [0 K9 p2 X1 K9 d0 h6 u7 [$ d8 ~
12, 0.182128906, 0.182617188, 0.182373047,0.000524211,
$ W6 I# Q+ \) ^& I' h 13, 0.182128906, 0.182373047, 0.182250977,-0.000086854,+ \1 B% Z9 V3 b) k
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发表于 2015-6-4 09:25:35