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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.m
7 y2 r. N0 ]/ l0 k U' @( ffunction[k,x,f_value]=Bisection(f,a,b,eps1,eps2,N)0 Y+ s1 I2 O2 d" ~5 L! f `
fprintf('k ,a ,b ,x, f\n')
5 @) N; A6 j, W9 }; j- ]for k=1:N
' Z/ v- K" A: E x=(a+b)/2;
0 E! M9 ~+ N: P/ ~* O f_value=f(x);
( O2 Q _# m- O, J" U- r' A3 ~ fprintf( '%3d, %10.9f, %10.9f, %10.9f,%10.9f,\n'...# m0 R) e+ Q: U8 l ?- o4 a
,k ,a ,b ,x, f_value). _5 t8 }. i8 l+ {$ C8 D
if abs(f_value)< eps1||0.5*(b-a)<eps2: c5 N, g8 z" F( p" b
return
4 g3 [' B+ K. q1 N else
- Z2 J5 I8 T. A0 c if f(x)*f(a)<02 D2 U9 n# F( W! Z
b=x;
$ h5 h+ o) G; `5 g. W! l" }2 v else
/ V5 C; N' q9 u8 F4 y' Q a=x;
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if k== N
: P* K* \+ j& y' |3 ]7 j v warning ('算法超出最大迭代数!')
& H8 F- ~7 K$ q" j end
* A3 ]+ u" {+ e: E1 L; l* G end
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a=0; b=1;
! K6 B( l0 H1 ?2 }1 ]9 ieps1=1e-4;eps2=1e-4;2 Z4 G$ B# i9 x- S
N=300;
2 C* j7 [3 x; i1 c1 U7 x5 Ef=@ (x) (x^3-3*x^2+6*x-1);
; `) F, k6 T; i/ [0 B% W! g3 q) cHfun=@Bisection;
6 b. u/ d! K4 Z p[k,x,f_value]= feval(Hfun, f,a,b,eps1,eps2,N);- @ _; w: R/ v
9 M' w, P* C) P6 ]0 h运行结果
5 t) B2 J) B; u7 p V% y; K; v>> examlpe71 t3 A. x- F8 M( K$ T: R
k ,a ,b ,x, f% h: C& p9 G3 S* q7 P
1, 0.000000000, 1.000000000, 0.500000000,1.375000000,/ c+ L$ s& @) g9 x I& W: m6 O; M# i
2, 0.000000000, 0.500000000, 0.250000000,0.328125000,; p$ y; d3 ~1 I' W. t
3, 0.000000000, 0.250000000, 0.125000000,-0.294921875,6 Y2 m! o; X* d3 G+ C( j: y2 A# w
4, 0.125000000, 0.250000000, 0.187500000,0.026123047,
4 D! t3 d- x1 U8 \ 5, 0.125000000, 0.187500000, 0.156250000,-0.131927490,) n9 K: [, s T) u8 Q$ X8 x
6, 0.156250000, 0.187500000, 0.171875000,-0.052295685,
7 n6 w* I0 W% }7 F, \# C T4 p, _ 7, 0.171875000, 0.187500000, 0.179687500,-0.012936115,
" Q4 |+ r) k* k& }1 h, } 8, 0.179687500, 0.187500000, 0.183593750,0.006630838,
! \! L9 l: d2 N6 Z: T' a 9, 0.179687500, 0.183593750, 0.181640625,-0.003143273,3 j2 X9 U! r. C9 V% a% F0 m
10, 0.181640625, 0.183593750, 0.182617188,0.001746121,
2 b7 i5 \2 |* |( q; P 11, 0.181640625, 0.182617188, 0.182128906,-0.000697991,+ q6 e. Y( i! y6 I
12, 0.182128906, 0.182617188, 0.182373047,0.000524211,
* y5 M! `" z- z 13, 0.182128906, 0.182373047, 0.182250977,-0.000086854,
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发表于 2015-6-4 09:25:35