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解方程的二分法 matlab 程序 （ x^3-3*x^2+6*x-1=0）( A4 T: ~2 c0 P' Q8 \! {: l2 L
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% Bisection.m
: C% O& [, g; N2 rfunction[k,x,f_value]=Bisection(f,a,b,eps1,eps2,N)2 V. l! t3 R1 `* d
fprintf('k ,a ,b ,x, f\n')
0 o; ]# z9 Y8 D; @1 U6 K, _for k=1:N
# J' P& U+ `! M4 ]9 W x=(a+b)/2;
5 ]4 r4 l' X: ~1 T) q& @1 k f_value=f(x);; w1 W3 S3 y' f' T( w( A7 F4 X
fprintf( '%3d, %10.9f, %10.9f, %10.9f,%10.9f,\n'...
% K2 y9 S* @ G0 f ,k ,a ,b ,x, f_value)
* s f; ]9 i2 m8 k' a/ N if abs(f_value)< eps1||0.5*(b-a)<eps26 Z' u0 s# f# z% P6 I# H
return# c1 Y0 L2 \: m7 ~5 E$ C& W& u
else
! f- B5 B7 ?( I# D if f(x)*f(a)<0+ x- V! K% h6 N8 l8 H/ R8 x8 X; W
b=x;
: L$ ^9 U4 ]; F4 ?* T else: Q* T% y; P) e; N4 ~
a=x;
1 j8 T* }# b$ K end
) O9 U! s+ u6 b/ Y% Y$ Y; D+ \2 T' B if k== N
2 y# L, u1 \, a6 p L warning ('算法超出最大迭代数!')
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end. n: [9 A5 f2 U
G8 ]1 [) T$ x) s6 f! L% examlpe7.m
, i- F0 J a Y3 M* q+ d+ Ha=0; b=1;: K/ \% @4 t6 s8 [1 h4 ]* E: P
eps1=1e-4;eps2=1e-4;
: p' L2 B ^$ |& @9 C$ |- k4 W N=300;
+ ^* K$ `4 \5 ?4 O: Zf=@ (x) (x^3-3*x^2+6*x-1);( W- M1 N( s0 t' w
Hfun=@Bisection;. s7 b; B( ^/ m. a. a$ k4 q" o6 P) M
[k,x,f_value]= feval(Hfun, f,a,b,eps1,eps2,N);
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0 U& T% ?7 s# P" n& Q运行结果
/ I) Q& Q6 h# J0 z; s/ y>> examlpe7
. E* p: Z* S( a7 S9 ^; Sk ,a ,b ,x, f
* ?: S, \; s5 w) o& k# u u9 \, |+ J0 R 1, 0.000000000, 1.000000000, 0.500000000,1.375000000,
/ d t1 p, K, V! q( M8 w 2, 0.000000000, 0.500000000, 0.250000000,0.328125000,
* V( l* r- ~. D 3, 0.000000000, 0.250000000, 0.125000000,-0.294921875,! Q4 M7 ]0 G1 s. u
4, 0.125000000, 0.250000000, 0.187500000,0.026123047,
/ S( R+ g" O1 X4 a8 W8 Q 5, 0.125000000, 0.187500000, 0.156250000,-0.131927490,
4 g: H9 i/ F# P0 N4 ]& {* S 6, 0.156250000, 0.187500000, 0.171875000,-0.052295685,0 f( T( L! Z4 [, G
7, 0.171875000, 0.187500000, 0.179687500,-0.012936115,6 P; n/ K# V4 I9 V
8, 0.179687500, 0.187500000, 0.183593750,0.006630838,+ p# P" D! d8 ^4 t
9, 0.179687500, 0.183593750, 0.181640625,-0.003143273,$ _* l t* v, g5 K
10, 0.181640625, 0.183593750, 0.182617188,0.001746121,
/ t0 E& L8 R, [9 x; Y% V% j5 L0 W 11, 0.181640625, 0.182617188, 0.182128906,-0.000697991,2 T4 r% l0 |1 i: \9 H
12, 0.182128906, 0.182617188, 0.182373047,0.000524211,
5 @9 W/ U. o, z: ?; D 13, 0.182128906, 0.182373047, 0.182250977,-0.000086854,* |/ }3 k+ R# Z% r* s
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发表于 2015-6-4 09:25:35