[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;close5 R* S* A# I\" m
% n=input('请输入迭代次数：');- K7 j; i0 f8 Q* M1 j; R
% qujian=input('请输入初始区间：');+ T, E1 N' ^3 W+ E! F3 j\" U
n=100;
) X' e% n3 d& m7 ?8 ]1 \
wucha=0.005;
, @& b. T7 L6 B, L# [
qujian=[0 1];
' A7 e! i6 ]+ K
a(1)=qujian(1);
% b: c! e. q5 \4 F1 Y
b(1)=qujian(2);
K7 |* s& Z% s) _
a0=a(1);
/ @) j* ~3 _4 A& G
b0=b(1);
. v% b% p! N& L& \( j2 M* h
x=qujian;
1 r8 d( c3 u/ D: @0 j8 I& Q- {3 t
y=exp(x)+10*x-2;
5 B2 b% z) R7 P1 J\" b$ L\" G
y1=y(1); %小于08 H H8 Q, _+ {7 j6 g
y2=y(2); %大于0
7 d$ `' S9 k5 t& T( @5 k
for i=1:n %总迭代次数
# t7 | v7 P! e' x/ A% z4 e6 V
c(i)=(a+b)/2;- h4 ?% X* K B. {( x
f(i)=exp(c(i))+10*(c(i))-2;/ ]5 o% G b7 {7 a# U0 W7 T( A
kesai_k(i)=(b-a)/2;
' R% P$ g* F, V! W& t- T
if f(i)>0
. _+ z ^0 v1 q+ {0 g
b=c(i);$ l, E3 u+ s, k' ?* f* s
b1(i)=c(i);
* t8 _8 D+ R, Z2 C4 q, ?
a1(i)=a;
8 z* x9 l5 d p6 O
elseif f(i)<0
8 R) m) M, q2 n6 P- r+ u' F\" V E
a=c(i);6 o5 G0 Y: K1 N- @
a1(i)=c(i);. r8 x. ]. y4 W; u\" G* _2 R
b1(i)=b;7 B. T4 R9 t5 [1 v/ m/ P! d
elseif f(i)==0||kesai_k(i)<=wucha
' C$ w: h! y# B% k p4 _
disp('精确值解为：');/ x/ k% m8 D* k3 E) Y
disp(c(i));
# d( K: K9 s& a4 y) z
break;. A( `) X! w2 T, K
end. X. `9 y6 G% ^$ t
end
* H2 l3 C1 J+ R\" P$ E$ Y: R
disp('迭代次数：');
: b/ ^/ \9 Z c4 j( B* c1 B5 s4 r/ c
fprintf('%d次\n\n',n);
6 B3 s4 Z3 Y% j; t\" V\" }
fprintf('要求误差%f\n\n',wucha);
* |/ T, w! g; C4 n4 {2 R! G8 H
disp('输出矩阵为：');
/ t# P+ u- o3 M9 Z: p0 F. E
A=[a0 a1]';2 ]- D, M; R+ o7 d3 A
B=[b0 b1]';. Y9 K8 _: z% B
format long# z: p) V1 l1 X' P3 y$ y\" v
data_out=[A B c' f' kesai_k']\" f, L) u5 o& N& g. [) B5 Q
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：4 N4 S# k% E k( f
0.0905
+ C+ R1 f% y5 T) Q* a
' Z% z8 y6 Z* ]! @\" d1 V( D- E
迭代次数：+ H! x' r1 ?; G3 f
100次
+ v* j5 A* |\" r6 K% J
% n1 m, }- h\" Q9 c. p9 x! T
要求误差0.005000
^8 `0 S\" _& d1 b- U3 p
+ {+ K- [( d4 J
输出矩阵为：
- T# K! V; s7 q2 l\" N
, C9 e4 C1 [! y5 H( [/ f\" n& B# T
data_out =' M0 c( h9 \+ b; j
+ K: B4 G: z) o& e) y0 z& R+ M
0 1.000000000000000 0.500000000000000 4.648721270700128 0.500000000000000 }/ B3 Z8 O8 ?
0 0.500000000000000 0.250000000000000 1.784025416687741 0.250000000000000
1 M M+ b# {\" r% O. H, r
0 0.250000000000000 0.125000000000000 0.383148453066826 0.125000000000000
. S( R7 F5 V' O7 o {6 v- S6 Q% y
0 0.125000000000000 0.062500000000000 -0.310505541082140 0.062500000000000
; i) @2 V& N6 E: B
0.062500000000000 0.125000000000000 0.093750000000000 0.035785140307826 0.031250000000000
6 v1 @1 \/ u) `9 r4 @
0.062500000000000 0.093750000000000 0.078125000000000 -0.137492192550960 0.015625000000000
5 w! ]2 ]# h* v0 m8 r/ ?$ T, N ^
0.078125000000000 0.093750000000000 0.085937500000000 -0.050886782461907 0.0078125000000009 J( _% c6 N' f# L+ r6 z
0.085937500000000 0.093750000000000 0.089843750000000 -0.007559167670695 0.003906250000000
5 A\" j b9 L$ J6 k3 G9 \\" t- L
0.089843750000000 0.093750000000000 0.091796875000000 0.014110895592678 0.001953125000000* r. g9 L J. B% B1 t7 m( r
0.089843750000000 0.091796875000000 0.090820312500000 0.003275341789827 0.000976562500000$ L X' `& G, e, s
0.089843750000000 0.090820312500000 0.090332031250000 -0.002142043419492 0.000488281250000
$ D# F; Y+ N! y7 f
0.090332031250000 0.090820312500000 0.090576171875000 0.000566616557439 0.0002441406250001 A, A$ B, Q5 n
0.090332031250000 0.090576171875000 0.090454101562500 -0.000787721586963 0.0001220703125002 N V$ i' m5 _+ H w8 `& ~
0.090454101562500 0.090576171875000 0.090515136718750 -0.000110554553871 0.000061035156250
5 \6 s/ W8 S; W% y( L, g' a& x
0.090515136718750 0.090576171875000 0.090545654296875 0.000228030491991 0.0000305175781254 j, q C* d9 q ^/ g x$ z
0.090515136718750 0.090545654296875 0.090530395507813 0.000058737841614 0.000015258789063
, @/ P/ ^2 n4 l! s) ^: ]& {
0.090515136718750 0.090530395507813 0.090522766113281 -0.000025908387990 0.000007629394531- u9 a! @, R& k0 L: K' K
0.090522766113281 0.090530395507813 0.090526580810547 0.000016414718847 0.000003814697266
; c9 U7 w% a- v$ R6 f/ I
0.090522766113281 0.090526580810547 0.090524673461914 -0.000004746836563 0.000001907348633 W0 M- D% T2 A# y3 x% ]5 D! z& @
0.090524673461914 0.090526580810547 0.090525627136230 0.000005833940644 0.000000953674316
9 u! H; d* I% U
0.090524673461914 0.090525627136230 0.090525150299072 0.000000543551916 0.000000476837158
5 z5 J\" B# l& @
0.090524673461914 0.090525150299072 0.090524911880493 -0.000002101642354 0.000000238418579) D0 k: A3 u/ N) t2 O
0.090524911880493 0.090525150299072 0.090525031089783 -0.000000779045227 0.000000119209290
' G0 |! S9 X6 m2 }1 S5 Q8 N
0.090525031089783 0.090525150299072 0.090525090694427 -0.000000117746657 0.000000059604645; w- {$ | R3 U
0.090525090694427 0.090525150299072 0.090525120496750 0.000000212902629 0.000000029802322, }1 s. \% g B* m
0.090525090694427 0.090525120496750 0.090525105595589 0.000000047577986 0.000000014901161
9 o5 I. R\" ?% T% {
0.090525090694427 0.090525105595589 0.090525098145008 -0.000000035084336 0.000000007450581
2 X- u$ m- l5 t$ N' v+ ~
0.090525098145008 0.090525105595589 0.090525101870298 0.000000006246825 0.000000003725290
\" h& d* w; x! ~
0.090525098145008 0.090525101870298 0.090525100007653 -0.000000014418755 0.0000000018626454 m# {# g& ^( L/ R9 u( I* q
0.090525100007653 0.090525101870298 0.090525100938976 -0.000000004085965 0.000000000931323
w$ [: f3 m9 j! ^+ @- @# F
0.090525100938976 0.090525101870298 0.090525101404637 0.000000001080430 0.000000000465661- N3 N. M' C- ^* B
0.090525100938976 0.090525101404637 0.090525101171806 -0.000000001502767 0.000000000232831
|9 F# K f. `$ V
0.090525101171806 0.090525101404637 0.090525101288222 -0.000000000211169 0.000000000116415
+ Y5 l& `& x& h1 y/ b' {7 ?
0.090525101288222 0.090525101404637 0.090525101346429 0.000000000434631 0.0000000000582088 O3 E( m, e2 t3 T4 F
0.090525101288222 0.090525101346429 0.090525101317326 0.000000000111731 0.000000000029104) Y5 j0 _& x6 c$ @, G
0.090525101288222 0.090525101317326 0.090525101302774 -0.000000000049719 0.000000000014552
$ e5 }* a& C; E6 {2 @$ X0 x/ `. C
0.090525101302774 0.090525101317326 0.090525101310050 0.000000000031006 0.000000000007276
; I5 [& h. a\" }
0.090525101302774 0.090525101310050 0.090525101306412 -0.000000000009357 0.000000000003638- Z& [8 Q5 h o3 [
0.090525101306412 0.090525101310050 0.090525101308231 0.000000000010825 0.000000000001819
- k6 ~' N% |5 } \3 c
0.090525101306412 0.090525101308231 0.090525101307321 0.000000000000734 0.000000000000909
2 W: b# H- M9 a\" k& G
0.090525101306412 0.090525101307321 0.090525101306866 -0.000000000004311 0.000000000000455
3 I5 j; N+ |; q3 [& o
0.090525101306866 0.090525101307321 0.090525101307094 -0.000000000001789 0.000000000000227
. j% }$ f) R3 s6 {) u2 ?
0.090525101307094 0.090525101307321 0.090525101307207 -0.000000000000527 0.000000000000114' }4 f4 X# x\" s9 z
0.090525101307207 0.090525101307321 0.090525101307264 0.000000000000103 0.000000000000057\" i3 Q/ E& o5 X1 `( E5 J2 r
0.090525101307207 0.090525101307264 0.090525101307236 -0.000000000000212 0.000000000000028 `. M, B8 g7 T3 E
0.090525101307236 0.090525101307264 0.090525101307250 -0.000000000000054 0.000000000000014# N# i( c0 d4 Q6 P
0.090525101307250 0.090525101307264 0.090525101307257 0.000000000000025 0.0000000000000071 E4 J0 m8 Y3 I- j# g/ ~
0.090525101307250 0.090525101307257 0.090525101307254 -0.000000000000015 0.000000000000004+ D5 S. }5 _: f2 P, @& v A2 A
0.090525101307254 0.090525101307257 0.090525101307255 0.000000000000005 0.000000000000002
: c\" g7 K- `' R0 `5 v' M0 B' k
0.090525101307254 0.090525101307255 0.090525101307255 -0.000000000000005 0.000000000000001
) _; [; }1 l6 y* J% f- B& |
0.090525101307255 0.090525101307255 0.090525101307255 0 0.000000000000000