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解方程的二分法 matlab 程序 ( x^3-3*x^2+6*x-1=0) f5 O3 n/ X% M5 q9 k# W
# c: I5 t! g( Z$ {( Z
% Bisection.m- z/ g; \7 t, _' B8 n* R- {
function[k,x,f_value]=Bisection(f,a,b,eps1,eps2,N); `4 C/ W: Y7 _3 H: O+ f
fprintf('k ,a ,b ,x, f\n')7 O O8 l9 W: B' H
for k=1:N( \/ Y* a! C6 H6 Q4 A
x=(a+b)/2;" m. T: f+ Y$ K3 m& q t
f_value=f(x);6 K# Q1 o& @- q m H$ i5 F, {- H
fprintf( '%3d, %10.9f, %10.9f, %10.9f,%10.9f,\n'...& d! _& d. b6 K* h7 C4 W8 j6 @2 _) Z
,k ,a ,b ,x, f_value)
+ q: j3 D! b8 j! l7 G if abs(f_value)< eps1||0.5*(b-a)<eps2! e! u# j7 v1 l8 u
return
0 g' L0 P+ @# \ else
6 f/ C9 @- l) a& c8 @ if f(x)*f(a)<0
% `, n4 ], C! G3 b b=x;
, i& i9 D. o6 ]/ T' N else- S8 A7 D7 w$ W" I" X
a=x;# g7 R9 @& k) z0 V! D. y
end ~6 a7 ]4 R4 |+ P/ | C4 n
if k== N
+ ^8 @ S5 O' S: y5 |- S+ } warning ('算法超出最大迭代數!') $ q* F, n8 q- v- X* [3 `) J
end
/ e. M+ v" j- A2 ?+ h1 W7 y- m* Q end
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% examlpe7.m( q( C @" P% _
a=0; b=1;6 |7 t4 b6 ^: h: F- O* ]5 h
eps1=1e-4;eps2=1e-4;% y. V( V/ Y5 F7 A( c9 T
N=300;8 ~3 F3 ]4 @: E. Z
f=@ (x) (x^3-3*x^2+6*x-1);
# k# X1 M/ ?; YHfun=@Bisection;
1 e1 r: p" g6 o |% B# D5 o[k,x,f_value]= feval(Hfun, f,a,b,eps1,eps2,N);
# q" V" b: H. [ H2 E2 Q& l6 f( V- A
運行結果
. a* g3 o4 u& f. M9 |; }>> examlpe7
; ~+ L8 O: h" Y1 p! Rk ,a ,b ,x, f j& [, d! |) p0 m) ?
1, 0.000000000, 1.000000000, 0.500000000,1.375000000,
# Y* q$ x2 I' N& U/ _: h. _# A 2, 0.000000000, 0.500000000, 0.250000000,0.328125000,6 J' K8 E1 D f& m
3, 0.000000000, 0.250000000, 0.125000000,-0.294921875,# K1 i$ f! Z3 B0 X
4, 0.125000000, 0.250000000, 0.187500000,0.026123047,
: v8 m$ I8 F; Q+ ?; ~/ Q. Y 5, 0.125000000, 0.187500000, 0.156250000,-0.131927490,- Z+ H& L" p: ?- }0 }* _2 {' {* }# _! d
6, 0.156250000, 0.187500000, 0.171875000,-0.052295685,5 V4 p' _4 U0 H& p
7, 0.171875000, 0.187500000, 0.179687500,-0.012936115,0 Y' t2 O6 ]5 U- N& v8 E1 i
8, 0.179687500, 0.187500000, 0.183593750,0.006630838,
8 Z' ^" m# G6 ` 9, 0.179687500, 0.183593750, 0.181640625,-0.003143273,
2 \! b8 Q8 K( h4 M+ x 10, 0.181640625, 0.183593750, 0.182617188,0.001746121,' I+ A. U- D U" P
11, 0.181640625, 0.182617188, 0.182128906,-0.000697991,7 J3 u6 s: @* ]" t$ w. L' K
12, 0.182128906, 0.182617188, 0.182373047,0.000524211,
M) O V$ \ z2 S" Z) ]1 b 13, 0.182128906, 0.182373047, 0.182250977,-0.000086854,; g" w, t; H- [! L$ V+ V
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