[代码资源] 用对分法解超越方程

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发表于 2016-10-12 23:05 |只看该作者 |倒序浏览

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范例：用对分法求方程在(0,1)内的根，要求误差不超过0.1；
求解程序如下：

clear;clc;close1 L7 j: z7 P0 |: e
% n=input('请输入迭代次数：');
, O: O% n& g2 C4 V4 S
% qujian=input('请输入初始区间：');
8 a+ n1 ]! M; z: j
n=100;\" ]\" w- d: Y. _, T: ?% h3 Q. c
wucha=0.005;; m6 i7 ?) \1 V+ J$ t
qujian=[0 1];5 p, v, s7 ~1 }. |, s8 s! a& z$ v# V
a(1)=qujian(1);
: n% \, L$ B) i) ?: c
b(1)=qujian(2); ; x\" F/ |3 w+ O$ `$ }. C2 l6 M
a0=a(1);
7 ]6 w8 r% L D6 W! K
b0=b(1);
% ]3 q; U; V) D2 u( k) N. C
x=qujian;
4 {/ r/ o) {/ ?0 \8 g' C4 o\" B
y=exp(x)+10*x-2;
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y1=y(1); %小于0' u/ q2 T X% D. h
y2=y(2); %大于0
for i=1:n %总迭代次数
* D6 y1 s/ M4 Z2 y
c(i)=(a+b)/2;4 M+ F# D+ o- l4 ~5 _& q r6 c
f(i)=exp(c(i))+10*(c(i))-2;: h4 D( I4 g4 A1 @: E! W' {
kesai_k(i)=(b-a)/2;
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if f(i)>0
, I4 U! c; }) `% c# E
b=c(i);
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b1(i)=c(i);
- ~, i8 S3 f! G
a1(i)=a;5 L4 k h7 e3 d h8 n# Q) h3 a0 T
elseif f(i)<0+ P U\" E2 v( _' K1 i6 |
a=c(i);
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a1(i)=c(i);
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b1(i)=b;
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elseif f(i)==0||kesai_k(i)<=wucha
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disp('精确值解为：');
& s\" y$ r4 c) @. K8 W3 \6 k
disp(c(i));
3 p7 V8 p+ J1 n4 H$ n. i\" r
break;
2 {# Q\" Q: O0 j7 e
end4 g3 n) T6 @& ?3 t
end( `1 B& c\" @8 |
disp('迭代次数：');
7 Q0 O2 W. R( ?1 A% h O$ x$ [+ }
fprintf('%d次\n\n',n);
* {. f\" V4 z# _
fprintf('要求误差%f\n\n',wucha);, N* u6 m2 Q, v( D- l- I/ k
disp('输出矩阵为：');
) f0 R3 h) |6 b! V5 {9 I
A=[a0 a1]';/ ]4 U! m1 p; g$ E- l
B=[b0 b1]';8 \; p# |\" A/ K( g0 o) T- ]# {
format long
8 l' F, |/ ~& P$ G% v9 m
data_out=[A B c' f' kesai_k']7 q6 @: H4 E: a) l) U9 t) c/ c
xlswrite('二分法处理数据.xls',data_out);

复制代码

结果输出情况：

精确值解为：6 Z$ g' _* G8 K
0.0905
6 d% h P. T) L
! K: N) @; [* Z9 ]' Z% R! x. w
迭代次数：8 r r' |5 _7 @& q& B0 `
100次. G- t+ ` F\" G& H( o
& _2 }. b! v% G+ l6 _7 T
要求误差0.005000
6 |5 }2 A5 G! h/ k
* z! y8 d& L; [# H! E
输出矩阵为：9 Q. Y/ H/ M q% ?* W/ s+ v& W
% s* u6 ?4 Q3 z
data_out =
/ U5 o! l6 a* O( @\" z: C0 z
' L$ u K! U' M/ z- R3 Y: c
0 1.000000000000000 0.500000000000000 4.648721270700128 0.5000000000000004 F# `% W% X6 D$ H# h, i\" Z* \' g0 X
0 0.500000000000000 0.250000000000000 1.784025416687741 0.250000000000000! k2 B* n1 J/ l5 ~' a; R0 m7 g
0 0.250000000000000 0.125000000000000 0.383148453066826 0.125000000000000
; J* q; C# V9 z4 Q1 i$ {! r6 j; U
0 0.125000000000000 0.062500000000000 -0.310505541082140 0.062500000000000
6 I$ U- u4 x2 o4 d# {1 b
0.062500000000000 0.125000000000000 0.093750000000000 0.035785140307826 0.031250000000000
. P\" e* d7 q; X2 |; R! {9 j2 A
0.062500000000000 0.093750000000000 0.078125000000000 -0.137492192550960 0.015625000000000
' h A: p; x# m3 P: a2 R
0.078125000000000 0.093750000000000 0.085937500000000 -0.050886782461907 0.007812500000000
8 e5 @' H( u7 u: n6 ]' G w( K
0.085937500000000 0.093750000000000 0.089843750000000 -0.007559167670695 0.003906250000000* s9 M4 J# }+ o- i
0.089843750000000 0.093750000000000 0.091796875000000 0.014110895592678 0.0019531250000000 G8 x3 S: I: a: ~- T& J
0.089843750000000 0.091796875000000 0.090820312500000 0.003275341789827 0.000976562500000
$ Y1 B7 c5 R. x
0.089843750000000 0.090820312500000 0.090332031250000 -0.002142043419492 0.000488281250000: s\" O2 F6 f! ~
0.090332031250000 0.090820312500000 0.090576171875000 0.000566616557439 0.000244140625000
2 O) Q- O+ ] X) l
0.090332031250000 0.090576171875000 0.090454101562500 -0.000787721586963 0.0001220703125000 \/ D. a, N+ e0 j \$ h8 u
0.090454101562500 0.090576171875000 0.090515136718750 -0.000110554553871 0.000061035156250
- I$ M6 {, Z! u1 H
0.090515136718750 0.090576171875000 0.090545654296875 0.000228030491991 0.000030517578125
3 _. {. t, w0 ]/ N( f0 @1 v8 N
0.090515136718750 0.090545654296875 0.090530395507813 0.000058737841614 0.000015258789063& C3 S& e) X2 K: W\" `6 K7 j
0.090515136718750 0.090530395507813 0.090522766113281 -0.000025908387990 0.000007629394531
# G3 V5 k4 [6 p2 \) O# V
0.090522766113281 0.090530395507813 0.090526580810547 0.000016414718847 0.000003814697266; G0 s8 f f7 W
0.090522766113281 0.090526580810547 0.090524673461914 -0.000004746836563 0.0000019073486339 s4 P+ w# e7 ^; b7 P1 \5 N
0.090524673461914 0.090526580810547 0.090525627136230 0.000005833940644 0.000000953674316
3 H- s\" x, K/ c. e0 u4 s/ x
0.090524673461914 0.090525627136230 0.090525150299072 0.000000543551916 0.000000476837158
4 {; v& h9 k2 p, f x6 W
0.090524673461914 0.090525150299072 0.090524911880493 -0.000002101642354 0.000000238418579
5 i( c% Q( Q% `' J8 H8 c! S7 n
0.090524911880493 0.090525150299072 0.090525031089783 -0.000000779045227 0.000000119209290. P4 l' j% G/ i- c+ B$ T, j
0.090525031089783 0.090525150299072 0.090525090694427 -0.000000117746657 0.000000059604645
3 B+ B0 o\" t6 F, p; E, M
0.090525090694427 0.090525150299072 0.090525120496750 0.000000212902629 0.000000029802322 U, m0 k0 m; c
0.090525090694427 0.090525120496750 0.090525105595589 0.000000047577986 0.000000014901161
9 t: |2 s+ E! i5 h
0.090525090694427 0.090525105595589 0.090525098145008 -0.000000035084336 0.0000000074505811 h8 Y' n1 t+ r' F: e
0.090525098145008 0.090525105595589 0.090525101870298 0.000000006246825 0.000000003725290
, G8 ~% D, D0 [# I; d& B5 w
0.090525098145008 0.090525101870298 0.090525100007653 -0.000000014418755 0.0000000018626455 m- R2 C V+ O- o
0.090525100007653 0.090525101870298 0.090525100938976 -0.000000004085965 0.000000000931323
! J, y: c/ o; p. Y: e
0.090525100938976 0.090525101870298 0.090525101404637 0.000000001080430 0.000000000465661
6 [% f7 u/ z! L Y
0.090525100938976 0.090525101404637 0.090525101171806 -0.000000001502767 0.0000000002328315 E* d) ] o9 _# C6 t' W& O
0.090525101171806 0.090525101404637 0.090525101288222 -0.000000000211169 0.000000000116415# Z' Z' M, I0 l4 L6 _9 o
0.090525101288222 0.090525101404637 0.090525101346429 0.000000000434631 0.000000000058208
2 U6 }1 b- w Q+ Y& O\" `3 d* ~
0.090525101288222 0.090525101346429 0.090525101317326 0.000000000111731 0.000000000029104, x u6 f2 J7 Q% q8 W% \
0.090525101288222 0.090525101317326 0.090525101302774 -0.000000000049719 0.0000000000145528 ]& |) m( j9 V0 M
0.090525101302774 0.090525101317326 0.090525101310050 0.000000000031006 0.000000000007276
& X; A# q, D/ }9 c0 a0 H: X; s5 K& t
0.090525101302774 0.090525101310050 0.090525101306412 -0.000000000009357 0.0000000000036385 ~6 y: S\" ?\" L4 q0 `
0.090525101306412 0.090525101310050 0.090525101308231 0.000000000010825 0.000000000001819( f5 u' _8 A/ h( H) t3 p- @
0.090525101306412 0.090525101308231 0.090525101307321 0.000000000000734 0.000000000000909' M* {; z0 {0 O1 e9 h, H) r! N3 I+ m
0.090525101306412 0.090525101307321 0.090525101306866 -0.000000000004311 0.000000000000455
3 ~: h. _) L- w8 O0 A' v9 E, I, Y+ [
0.090525101306866 0.090525101307321 0.090525101307094 -0.000000000001789 0.000000000000227
/ O M$ h( s# H$ f
0.090525101307094 0.090525101307321 0.090525101307207 -0.000000000000527 0.000000000000114* A4 }- i/ c; d
0.090525101307207 0.090525101307321 0.090525101307264 0.000000000000103 0.000000000000057
+ c8 v6 v' N) H4 \' ^# l8 l' P* u* z
0.090525101307207 0.090525101307264 0.090525101307236 -0.000000000000212 0.000000000000028
& w9 x9 t& O: S) t( |6 t. T
0.090525101307236 0.090525101307264 0.090525101307250 -0.000000000000054 0.000000000000014
* Y9 u' ^( Y) v- v' c+ `
0.090525101307250 0.090525101307264 0.090525101307257 0.000000000000025 0.000000000000007
2 M- Q: Z. F4 _
0.090525101307250 0.090525101307257 0.090525101307254 -0.000000000000015 0.000000000000004
V# Q9 M$ Y6 ]6 v4 a l
0.090525101307254 0.090525101307257 0.090525101307255 0.000000000000005 0.000000000000002$ S4 W0 a3 g2 \\" w; Q% S5 T
0.090525101307254 0.090525101307255 0.090525101307255 -0.000000000000005 0.000000000000001. N3 Z6 }% r- x: F# T\" [
0.090525101307255 0.090525101307255 0.090525101307255 0 0.000000000000000