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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.m5 o9 k# x" n7 p e, G; s( ]7 ^
function[k,x,f_value]=Bisection(f,a,b,eps1,eps2,N), B8 I( E" @ C
fprintf('k ,a ,b ,x, f\n')) \) K! E7 ^1 c
for k=1:N9 v. {3 I5 ^! U( U# W) t3 }
x=(a+b)/2;
W( m- e% q2 F$ x5 r- I% q- k f_value=f(x);
) l0 w8 f5 {$ [5 _2 t: d9 g3 }# J- E fprintf( '%3d, %10.9f, %10.9f, %10.9f,%10.9f,\n'...
* I! J) F4 ?( D ,k ,a ,b ,x, f_value)
) L" t; v( P B1 ~ if abs(f_value)< eps1||0.5*(b-a)<eps22 K) P6 `% @1 r2 ^9 e
return
. k; x. A! f( O" v else
5 B: Q9 E/ E' R$ q* `: ^ if f(x)*f(a)<0
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else
/ h; X& D$ t& n; Q1 G) I7 o a=x;! l8 f2 j* ^7 b2 I8 }/ {6 g
end/ Y, N8 Y$ D! O; N% e, S# y
if k== N0 r; ?* P- [; m7 b4 i
warning ('算法超出最大迭代數(shù)!') ( c' C' R9 P5 y5 O
end
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% examlpe7.m8 |5 h) v$ ?+ {# ?
a=0; b=1;
8 S/ B& k0 f4 @! Peps1=1e-4;eps2=1e-4;
+ r/ ~7 d& C9 u6 J0 q- b% ` N=300;
( ]! p \& i9 S4 q- b4 ^! K" sf=@ (x) (x^3-3*x^2+6*x-1);
4 e8 J% M4 Y, E8 j9 |! H& dHfun=@Bisection;# z* s6 d& ~( @+ q/ y
[k,x,f_value]= feval(Hfun, f,a,b,eps1,eps2,N);
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運行結(jié)果
- J. S) Y; [+ N( _, H>> examlpe73 Y; f( Q9 k2 J% i# F
k ,a ,b ,x, f9 H# ?/ X: P4 r" D) {
1, 0.000000000, 1.000000000, 0.500000000,1.375000000,
( @ C& P- h* S0 {: ? 2, 0.000000000, 0.500000000, 0.250000000,0.328125000,
1 P' a4 B$ O4 }! `% k" v: o 3, 0.000000000, 0.250000000, 0.125000000,-0.294921875,1 Y) Y, R+ t' q* ], p7 e% \3 e
4, 0.125000000, 0.250000000, 0.187500000,0.026123047,% M' P2 p3 N8 v1 b/ r
5, 0.125000000, 0.187500000, 0.156250000,-0.131927490,
2 n$ n3 W4 E# U 6, 0.156250000, 0.187500000, 0.171875000,-0.052295685,0 c; [. {$ H/ B% ], v7 y, l* m
7, 0.171875000, 0.187500000, 0.179687500,-0.012936115,
6 x8 Q3 V8 Z; C 8, 0.179687500, 0.187500000, 0.183593750,0.006630838,
& |3 V J/ B! j/ Q2 c1 Y 9, 0.179687500, 0.183593750, 0.181640625,-0.003143273,- Y+ `$ j' K, r d. Y
10, 0.181640625, 0.183593750, 0.182617188,0.001746121,
' [' M; u% e6 B: K a6 U2 m. X 11, 0.181640625, 0.182617188, 0.182128906,-0.000697991,% {5 z) x+ |0 w$ A r# r& K" Z
12, 0.182128906, 0.182617188, 0.182373047,0.000524211, j: g% o! r. P' ?7 Q$ {4 x/ V
13, 0.182128906, 0.182373047, 0.182250977,-0.000086854,4 ]# A, D/ d1 s2 k0 X0 x
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發(fā)表于 2015-6-4 09:25:35
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