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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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3 \+ C: L; }# V8 c% Bisection.m+ P5 C$ L" R) X8 Y, [0 b- a& Q! K
function[k,x,f_value]=Bisection(f,a,b,eps1,eps2,N)2 J/ }1 |$ u7 t% ]2 c
fprintf('k ,a ,b ,x, f\n')$ R5 y2 f: y5 ^1 r: T% L
for k=1:N0 W+ m, I7 u+ B9 n2 A8 t3 j
x=(a+b)/2;" D# k3 J0 Q* |4 V
f_value=f(x);; G, p3 G' P$ B* q2 \
fprintf( '%3d, %10.9f, %10.9f, %10.9f,%10.9f,\n'...
5 p, o4 ]5 A7 W4 }: Y" s ,k ,a ,b ,x, f_value)
0 k7 ^3 H/ e4 f! C6 E" V if abs(f_value)< eps1||0.5*(b-a)<eps29 {' P0 h' ^- Z) h& O H
return# o w6 h$ x: I& s) \. K
else. e* Z! P* [! k4 Z& l
if f(x)*f(a)<0
* k c" K+ @* Y7 w1 Q$ _0 t; o b=x;
; H( q6 { j$ d( J else. J: b, J6 N9 q4 @% L
a=x;
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if k== N
7 B a! Q" t6 {3 b3 F! X0 a warning ('算法超出最大迭代數!') 5 ?" w: |0 f& x7 e n0 O. B3 o9 J
end
5 F5 X9 L$ I; b* }' P6 S& p0 f end
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# m) t$ N7 [$ L% H! O) _; ^% examlpe7.m
" S, J+ y9 c+ |( l2 @+ z8 i" Ha=0; b=1;( Q: Y( A4 F$ P# V
eps1=1e-4;eps2=1e-4;
* r5 M' c4 g2 a, r8 F/ ^5 a6 U; m N=300;
2 g+ E' }! w' L; Hf=@ (x) (x^3-3*x^2+6*x-1);9 G, R/ P- R6 \2 n
Hfun=@Bisection;
* q X9 g3 A' W[k,x,f_value]= feval(Hfun, f,a,b,eps1,eps2,N);
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2 H7 G9 k# o3 ^5 L. `+ b& v運行結果
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k ,a ,b ,x, f
9 ?, Q$ I Z o+ ?1 R, @ 1, 0.000000000, 1.000000000, 0.500000000,1.375000000,
$ K1 j/ f* Z. Y* [0 ^" g5 q 2, 0.000000000, 0.500000000, 0.250000000,0.328125000,# U: V; k+ U3 [1 w7 y( Y' o
3, 0.000000000, 0.250000000, 0.125000000,-0.294921875,
6 H, _$ Z7 m! Z 4, 0.125000000, 0.250000000, 0.187500000,0.026123047,, G/ L( c3 N4 o9 m
5, 0.125000000, 0.187500000, 0.156250000,-0.131927490,2 U* L6 K1 ?2 q9 D9 c; i) m
6, 0.156250000, 0.187500000, 0.171875000,-0.052295685,
* X% E7 d* m S 7, 0.171875000, 0.187500000, 0.179687500,-0.012936115,
. v" b! T8 d2 D 8, 0.179687500, 0.187500000, 0.183593750,0.006630838,8 I9 A7 c/ p1 }% r0 B
9, 0.179687500, 0.183593750, 0.181640625,-0.003143273,
0 f4 r5 L8 Z: }0 q) L/ [# O/ X 10, 0.181640625, 0.183593750, 0.182617188,0.001746121,
) Z3 w9 U' H5 h) a$ H' P. x0 J8 f 11, 0.181640625, 0.182617188, 0.182128906,-0.000697991,
% ]# S- y* \ w' `1 i2 @ 12, 0.182128906, 0.182617188, 0.182373047,0.000524211,- x$ o0 N# y; q `5 A; {$ ~
13, 0.182128906, 0.182373047, 0.182250977,-0.000086854,
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