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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 h; @1 \4 S5 H# i9 v B9 t0 @% Bisection.m
7 x; ~6 s) S6 Q4 N: N3 {; lfunction[k,x,f_value]=Bisection(f,a,b,eps1,eps2,N)+ R- E* ~ f1 a2 Y
fprintf('k ,a ,b ,x, f\n')6 d0 |- Z3 J( v3 ~
for k=1:N
5 F+ y' j# \ ?/ L2 K x=(a+b)/2;" b7 c: l& f7 G7 g! D3 @2 J7 P; e7 X
f_value=f(x);# g$ y* F( U) \2 T V! D
fprintf( '%3d, %10.9f, %10.9f, %10.9f,%10.9f,\n'...' ?5 s3 d, z" t1 G2 e7 i
,k ,a ,b ,x, f_value); w. g% @1 x1 V
if abs(f_value)< eps1||0.5*(b-a)<eps2; u+ |" l" s) `6 K9 k! h
return
4 t0 _ p, ]* F7 f3 J; c! | else
1 i- V+ o& `$ I if f(x)*f(a)<0
5 Z4 l1 ]9 _; R7 j4 L! t b=x;
8 k) c6 O3 _* r( \2 m% v else
/ K' |) [8 u* ` a=x;- h( r" Z: Y9 T/ z. a- h
end N1 Q9 K: j; j; w' e
if k== N' V! I7 Z+ o: O0 f# \
warning ('算法超出最大迭代数!') - M0 Q7 |" O8 F9 N* U7 C# h
end! e+ ?& m0 q$ J8 N" W6 {5 y
end
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% examlpe7.m
% Y2 f" G, p7 |- E& ^8 T: t3 ta=0; b=1;4 j3 A2 |; ?. l% d% d
eps1=1e-4;eps2=1e-4;
- h$ F' D* ]; b' b n* S, C N=300;3 Z' P' k" F6 {4 ?! T$ q
f=@ (x) (x^3-3*x^2+6*x-1);) M! [6 v1 v& b3 Y+ M
Hfun=@Bisection;
9 O5 X/ t' E! u1 p7 Q[k,x,f_value]= feval(Hfun, f,a,b,eps1,eps2,N);. h1 u9 L3 ~# {7 l
4 D* q& _1 r! t* g运行结果
5 l ]/ \( g; P>> examlpe7
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1, 0.000000000, 1.000000000, 0.500000000,1.375000000,
5 ]2 u Y) ~) d2 H) R( n9 O8 D 2, 0.000000000, 0.500000000, 0.250000000,0.328125000,% Y4 G. G' n4 l) P
3, 0.000000000, 0.250000000, 0.125000000,-0.294921875,
0 a, I+ N$ f2 J4 d7 V& o' Q; z 4, 0.125000000, 0.250000000, 0.187500000,0.026123047,
0 X9 \& K' i: P8 B3 e 5, 0.125000000, 0.187500000, 0.156250000,-0.131927490,7 V; K. n4 c& C$ V
6, 0.156250000, 0.187500000, 0.171875000,-0.052295685,
+ h& y( n' ~6 Y" y; I0 F0 C$ I" b 7, 0.171875000, 0.187500000, 0.179687500,-0.012936115,1 \6 V- n/ c5 v5 d4 M; [
8, 0.179687500, 0.187500000, 0.183593750,0.006630838,. M9 C! |) d# v# t2 K9 x& @
9, 0.179687500, 0.183593750, 0.181640625,-0.003143273,
# A( R, X& o1 o, P6 q, V' c$ v 10, 0.181640625, 0.183593750, 0.182617188,0.001746121,
8 ?; K6 g* @1 e9 t+ e 11, 0.181640625, 0.182617188, 0.182128906,-0.000697991,' f5 {( x! k2 Q* }" o Z- s+ i
12, 0.182128906, 0.182617188, 0.182373047,0.000524211,
' {& U/ ^* ~# t 13, 0.182128906, 0.182373047, 0.182250977,-0.000086854,
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