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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 G! h2 Y% f @" I) L/ h4 Q
function[k,x,f_value]=Bisection(f,a,b,eps1,eps2,N)2 V) t( R& I0 H: w# L
fprintf('k ,a ,b ,x, f\n')) ?, V+ o$ ]7 Z; X Z! J
for k=1:N y5 B0 _. c9 X
x=(a+b)/2;
6 T' I7 k7 C$ W f_value=f(x);( K9 T/ _6 ]7 X! M! Z3 Q
fprintf( '%3d, %10.9f, %10.9f, %10.9f,%10.9f,\n'...5 [6 T& L+ N: s! Y
,k ,a ,b ,x, f_value)
7 J* o( C4 N0 z( B, k$ C/ h7 x# F if abs(f_value)< eps1||0.5*(b-a)<eps2
; H7 a- w$ |7 [# m return
5 W: P9 c1 ^1 [2 o( J else
+ p4 L4 o; o; O& r if f(x)*f(a)<0
' G0 ]5 e0 c6 f% e3 ]4 o& _# R b=x;
4 z; N' L3 \" b else
9 @9 W3 A/ w7 i a=x;
" d/ m4 r2 Z, |; v. E% } end
2 F2 l* \5 B$ Y3 o6 a if k== N, B# u. b- X4 j+ Z0 r( u2 h
warning ('算法超出最大迭代數(shù)!')
3 m+ q% P% `% w; F& B end
( W5 [% v8 z6 T end
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% examlpe7.m& v+ X7 \6 d2 H- S
a=0; b=1;
2 C5 L1 K1 m: [5 j5 keps1=1e-4;eps2=1e-4;4 e% ~. g6 Z( P& C5 L% N& R$ u
N=300;5 {" z" W; A% m% o
f=@ (x) (x^3-3*x^2+6*x-1);
* U9 X) W5 \* r7 THfun=@Bisection;
+ Y3 \$ B' l7 ]' u" C[k,x,f_value]= feval(Hfun, f,a,b,eps1,eps2,N);( J! c+ f. X3 G: O( Z! R( X
% Z/ T8 z4 E) A2 [3 c1 t J8 D
運(yùn)行結(jié)果
' _6 L+ H+ I) a>> examlpe7, }/ P1 c. p- n" F& T. J
k ,a ,b ,x, f, v0 B p7 m: L/ A( X5 M' e9 O
1, 0.000000000, 1.000000000, 0.500000000,1.375000000,% a1 ?3 V7 A8 C2 E- B. B+ b
2, 0.000000000, 0.500000000, 0.250000000,0.328125000," Y* e8 \. f+ c* t& b% }3 Z
3, 0.000000000, 0.250000000, 0.125000000,-0.294921875,
+ I" A0 K! I. a( T2 v( D& n 4, 0.125000000, 0.250000000, 0.187500000,0.026123047,) q @& F& n: B3 ^, z
5, 0.125000000, 0.187500000, 0.156250000,-0.131927490, L) i7 N6 Z- ~" g' f
6, 0.156250000, 0.187500000, 0.171875000,-0.052295685,4 M6 Z3 K, `$ x2 V4 g/ N
7, 0.171875000, 0.187500000, 0.179687500,-0.012936115,, K( X J9 T6 i! a, ]3 ]6 w) U" K
8, 0.179687500, 0.187500000, 0.183593750,0.006630838,
3 }8 ^7 {& j. v5 t" Z 9, 0.179687500, 0.183593750, 0.181640625,-0.003143273,
# F1 n2 q- g) l- o+ }9 l 10, 0.181640625, 0.183593750, 0.182617188,0.001746121,
* u- E' |: p* Z 11, 0.181640625, 0.182617188, 0.182128906,-0.000697991,
2 F4 S5 g0 V7 C6 ^3 { 12, 0.182128906, 0.182617188, 0.182373047,0.000524211,
7 c. Y( |, W/ a5 o 13, 0.182128906, 0.182373047, 0.182250977,-0.000086854,
# }! B% u/ K2 k7 ^& |* v1 e `, e8 K( f. w
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