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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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5 f e7 ^: m7 b$ d) y; `5 d; k% Bisection.m
" K- Q% O0 |7 Q! R7 Vfunction[k,x,f_value]=Bisection(f,a,b,eps1,eps2,N)8 z k8 s U0 ] [$ O+ P( W
fprintf('k ,a ,b ,x, f\n')
- r" ?3 C/ @( ?- b( G* E! [for k=1:N
6 P8 B" }* i, ` x=(a+b)/2;* F2 J$ p$ n$ [3 V% J6 B! O' U0 q- r
f_value=f(x);, y8 Y8 G3 o: f) x) k) x6 T
fprintf( '%3d, %10.9f, %10.9f, %10.9f,%10.9f,\n'...
5 C. r' i g# P( @+ B4 j ,k ,a ,b ,x, f_value)
. A( _4 I7 [$ R; K7 p5 Q" x if abs(f_value)< eps1||0.5*(b-a)<eps2
4 D; C2 r) n. k/ N return" z4 L' L9 K% I* L/ d
else& c$ E8 X$ @8 \' T: L8 e
if f(x)*f(a)<0, ]( i$ s8 r2 D: d# U4 m! u+ u
b=x;9 Z9 I& u& i/ P5 f* ~
else+ K% V2 J* W+ y* ^# v
a=x;
/ ?0 S+ W0 A' L0 h' f1 Z3 P end
3 m9 @! [7 A+ h if k== N
1 Y4 a3 @0 c2 h1 z4 D- O+ T2 G4 j* @ warning ('算法超出最大迭代数!') - x/ \0 H! S9 y0 c3 o' Z) C
end& R( R T, \/ O9 d, W; r
end
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% examlpe7.m4 M4 B; ^* E" |/ x2 f
a=0; b=1;
4 F: k$ a+ U6 C5 p5 F' _* S. p1 oeps1=1e-4;eps2=1e-4;
0 C% D9 D+ c4 T' ?. { N=300;+ M4 R9 v: U8 p! A9 C* T/ ?, {
f=@ (x) (x^3-3*x^2+6*x-1);& F* m- K0 y. L0 t+ C5 m0 J8 F
Hfun=@Bisection;
9 L2 ?0 m c l1 x[k,x,f_value]= feval(Hfun, f,a,b,eps1,eps2,N);
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运行结果
. r8 J! C' N3 T2 t6 ]. d>> examlpe7# i% a9 n$ r/ C% K! g. {
k ,a ,b ,x, f- s3 r0 D* A( D5 G a3 V7 N7 P- v
1, 0.000000000, 1.000000000, 0.500000000,1.375000000,0 {! N/ R& i8 O' O# t }# H
2, 0.000000000, 0.500000000, 0.250000000,0.328125000,4 k* R c1 q) Q5 ^; G. v
3, 0.000000000, 0.250000000, 0.125000000,-0.294921875,
6 z/ S5 ~! d6 V% V4 U 4, 0.125000000, 0.250000000, 0.187500000,0.026123047,
8 g1 U& S& P1 Y6 Z0 L' {# g 5, 0.125000000, 0.187500000, 0.156250000,-0.131927490,
% ?% E4 `$ |( Y 6, 0.156250000, 0.187500000, 0.171875000,-0.052295685,
+ p0 R7 J. ?* |' A 7, 0.171875000, 0.187500000, 0.179687500,-0.012936115,4 v A9 A4 K& Y0 j/ E% K. O$ ^7 k
8, 0.179687500, 0.187500000, 0.183593750,0.006630838,
: j7 b1 A- V1 A+ K' G 9, 0.179687500, 0.183593750, 0.181640625,-0.003143273,
4 H3 m4 {2 h& f+ Z 10, 0.181640625, 0.183593750, 0.182617188,0.001746121,; S% f9 k' M3 Q% q8 r, x
11, 0.181640625, 0.182617188, 0.182128906,-0.000697991,
3 _3 I1 Z0 K0 m2 Q1 l) s" L 12, 0.182128906, 0.182617188, 0.182373047,0.000524211,
5 j# E& X3 S i" x$ O2 F$ e 13, 0.182128906, 0.182373047, 0.182250977,-0.000086854,# r$ K1 e: p/ p4 p2 l& x
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发表于 2015-6-4 09:25:35