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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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% Bisection.m1 z& e; ?& x. t7 I) E- W8 d1 w0 D
function[k,x,f_value]=Bisection(f,a,b,eps1,eps2,N). @/ i, `. l, s3 l% i) [6 t2 x- Q
fprintf('k ,a ,b ,x, f\n')
( ^( z4 x* Y/ W+ ]6 d+ t2 xfor k=1:N' e. C0 T- j0 `0 @. _* b
x=(a+b)/2;
: b! U" D* D2 E( j0 ~4 o f_value=f(x);7 N: ]- Z$ G% R: z. {) z8 R
fprintf( '%3d, %10.9f, %10.9f, %10.9f,%10.9f,\n'...
- E6 \, Y" U8 l. m6 Q+ E( o ,k ,a ,b ,x, f_value)
: |3 M2 f1 I+ h if abs(f_value)< eps1||0.5*(b-a)<eps2
7 e2 T. ]7 U3 i/ p: g3 H R3 | return
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if f(x)*f(a)<0# k9 H2 l4 Y3 J; c; g. |; A
b=x;
' R: D$ Y" `. r; O& g* y* a else
0 G+ a/ `! a$ y; g; c) C a=x;3 H3 ^, E5 v+ D: g5 d T: @, g
end
/ i! J2 k1 { b7 X$ ?: Q( {* X if k== N& C0 B4 J7 ?6 I _9 m9 }
warning ('算法超出最大迭代数!')
% w* b+ _$ K5 `$ Q7 R& `$ e' G end
9 R. E# s: `5 p, L end
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% examlpe7.m
' P' g N1 g! R/ h! M, ha=0; b=1;- ?1 i+ h2 o- u9 l# v; h: c; s
eps1=1e-4;eps2=1e-4;
0 y o( B7 ~' {1 U N=300;7 m/ \; @# \2 D' o! X
f=@ (x) (x^3-3*x^2+6*x-1);
% r l' t: G+ k6 y# O1 |Hfun=@Bisection;
J+ F- P- R* a/ `3 ^[k,x,f_value]= feval(Hfun, f,a,b,eps1,eps2,N);
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运行结果
, Z9 Q) k! d8 ^# I# w>> examlpe7
q" \0 b3 p( T* |k ,a ,b ,x, f* ^% i5 [/ ?$ h. C$ e/ S* {% E# x
1, 0.000000000, 1.000000000, 0.500000000,1.375000000,1 ~# F- {2 d4 X0 S6 X0 d* d) f: {( z8 j2 O
2, 0.000000000, 0.500000000, 0.250000000,0.328125000,
4 r% M' a$ _9 c6 k) s2 L 3, 0.000000000, 0.250000000, 0.125000000,-0.294921875,6 H# \+ K2 c, \- ~% x! z5 h' e
4, 0.125000000, 0.250000000, 0.187500000,0.026123047,+ I3 k( H+ T ], r& i \& W9 P
5, 0.125000000, 0.187500000, 0.156250000,-0.131927490,
$ @, W3 ^& D3 I; e& ?6 g 6, 0.156250000, 0.187500000, 0.171875000,-0.052295685,* ? C" U: Y# T) }
7, 0.171875000, 0.187500000, 0.179687500,-0.012936115,% K9 {" G2 h7 _! M+ q: H
8, 0.179687500, 0.187500000, 0.183593750,0.006630838,
! F, r& p7 o6 |; {3 X 9, 0.179687500, 0.183593750, 0.181640625,-0.003143273,9 N+ g4 H/ Y9 D8 |. t
10, 0.181640625, 0.183593750, 0.182617188,0.001746121,
; ~( `" J% S8 b2 a 11, 0.181640625, 0.182617188, 0.182128906,-0.000697991,
x$ h, Y' O4 b& l; |, K 12, 0.182128906, 0.182617188, 0.182373047,0.000524211,
# O' W4 L n6 W! }/ j( w 13, 0.182128906, 0.182373047, 0.182250977,-0.000086854," J/ q2 ^' R/ D
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发表于 2015-6-4 09:25:35