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解方程的二分法 matlab 程序 ( x^3-3*x^2+6*x-1=0)6 ], F/ n% m, @; O X
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% Bisection.m
% @# F$ w* @4 U+ Q: u+ w- p3 i. U) qfunction[k,x,f_value]=Bisection(f,a,b,eps1,eps2,N)9 D6 ^9 {6 m T* S+ ~0 K9 k
fprintf('k ,a ,b ,x, f\n')3 Q% |- D: o* r+ _. ?4 Q
for k=1:N7 x: d4 Y' G/ c+ \7 T) h
x=(a+b)/2;
2 d' C8 m' W! N9 z2 L& D f_value=f(x);
3 m7 |+ K* ^* @ @/ x+ t7 Y) B fprintf( '%3d, %10.9f, %10.9f, %10.9f,%10.9f,\n'...0 @, C! Y' g# l
,k ,a ,b ,x, f_value)
0 j* ?+ V, c7 u+ Z* i! x3 s1 h if abs(f_value)< eps1||0.5*(b-a)<eps23 H* d) J) y' P- A- b/ ^) q0 i& b
return' R# U* ]7 Y" W0 d- V
else1 _: R1 ~! g. m7 ]" n4 t" ^, V
if f(x)*f(a)<0
( B# B) e; \& |% v) Y) @ b=x;
6 B s5 Z3 I8 ]7 O2 ? else/ k" l7 o+ f( ?; k$ Z
a=x;
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if k== N- S1 N( R# n) ~
warning ('算法超出最大迭代数!') * B) L4 h+ E' V% T5 y
end3 D0 |5 p8 J+ ~( Q
end
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a=0; b=1;
+ [/ V0 |- T( _% }/ a# Ueps1=1e-4;eps2=1e-4;: y; |9 ?# l! O6 X
N=300;
$ R" P2 t8 ]5 s: q& hf=@ (x) (x^3-3*x^2+6*x-1);
- j- B6 l5 q$ { E# Q9 h1 ]Hfun=@Bisection; l* `: D+ S: T+ ]$ I$ k% O' r
[k,x,f_value]= feval(Hfun, f,a,b,eps1,eps2,N);( Z! @& r8 I' N& x+ o5 |( D
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运行结果
- K c8 u4 C h' K% x4 \# s; D% F>> examlpe73 y4 I1 d2 z2 i( Q! w
k ,a ,b ,x, f8 O. Q; v8 b& q
1, 0.000000000, 1.000000000, 0.500000000,1.375000000,
* Q, I0 Q" T q& r: c 2, 0.000000000, 0.500000000, 0.250000000,0.328125000,
0 S7 T) d3 U2 {, T8 o7 W: z 3, 0.000000000, 0.250000000, 0.125000000,-0.294921875,+ Q+ K5 D/ ^. p9 I: R: y
4, 0.125000000, 0.250000000, 0.187500000,0.026123047,( @: T( f s3 p. d* N
5, 0.125000000, 0.187500000, 0.156250000,-0.131927490, E/ m& ]; \, W9 w1 A
6, 0.156250000, 0.187500000, 0.171875000,-0.052295685,
( C0 O- ^- |% i% u* g2 ? 7, 0.171875000, 0.187500000, 0.179687500,-0.012936115,& _5 t: S2 t: N) ~3 P! i7 s+ @
8, 0.179687500, 0.187500000, 0.183593750,0.006630838,4 r+ ^' G9 }0 V3 E& Z
9, 0.179687500, 0.183593750, 0.181640625,-0.003143273,
% O: D% B5 X) U9 {' Z 10, 0.181640625, 0.183593750, 0.182617188,0.001746121,9 b6 n, E; r& z
11, 0.181640625, 0.182617188, 0.182128906,-0.000697991,4 ], B; U# H, i2 h0 q( u0 q
12, 0.182128906, 0.182617188, 0.182373047,0.000524211,
+ K5 b$ _0 u& R. a6 o) `; J 13, 0.182128906, 0.182373047, 0.182250977,-0.000086854,3 H& N) C+ p% L' X0 }
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