[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;close; z: v. r0 {% x; R8 i2 F
% n=input('请输入迭代次数：');) p c$ V! O9 e; i0 E\" U0 P\" b\" G. i
% qujian=input('请输入初始区间：');7 a4 i- B$ X6 @3 _
n=100;\" D) d( g r: H
wucha=0.005;
0 H7 @: x% q3 F* q+ w: `8 ~/ w; L
qujian=[0 1];
4 z' o) E% @& q+ B& b8 s+ I6 }, i
a(1)=qujian(1);0 n1 k: J\" R4 `
b(1)=qujian(2);
2 ?; ^) _- {. K* ] D0 f' R
a0=a(1);
3 `- |# y6 a' `' Y2 p# k) _
b0=b(1);6 @8 r9 s8 h \) b0 |
x=qujian;
+ I5 l3 P$ r8 l; }8 _& ^
y=exp(x)+10*x-2;/ X: x7 U8 G2 q/ Q2 ^ D. Q) H
y1=y(1); %小于0
2 D3 [3 X8 e2 F4 |\" v
y2=y(2); %大于08 _ W\" j. ^/ x5 ~4 R3 S7 A5 i
for i=1:n %总迭代次数\" q& s# F* O( c4 ^
c(i)=(a+b)/2;' r9 Y* y/ M\" q* X2 C. ]
f(i)=exp(c(i))+10*(c(i))-2;
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kesai_k(i)=(b-a)/2; e3 v) U. `$ W; F: Q4 t8 d
if f(i)>0
. a. [9 ^9 \$ R- R9 q
b=c(i);+ L G5 _& _! k. M! M5 {
b1(i)=c(i);\" w( {2 V' s# [8 [, u1 x6 E& j
a1(i)=a;
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elseif f(i)<0
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a=c(i);0 K4 I. c9 Y8 t- d/ p$ }
a1(i)=c(i);
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b1(i)=b;
7 c0 x9 ]& `8 t0 f
elseif f(i)==0||kesai_k(i)<=wucha# }. `. V$ ~1 b% P$ c& [$ s
disp('精确值解为：');( ], E! l8 |5 @/ C5 i
disp(c(i));
break;
\" Q5 o, I! C! v! R+ w9 G
end& C2 ^$ Z5 a7 s2 p: E8 {
end: f6 I2 V+ ]9 g# @6 s
disp('迭代次数：');1 e( n; v P% i# H% h
fprintf('%d次\n\n',n);
0 M8 ?8 s2 X8 x$ p7 i
fprintf('要求误差%f\n\n',wucha);
' e) n2 @! x ^( R) o
disp('输出矩阵为：');
' w7 Z$ h6 x6 g% u7 ^& E& X
A=[a0 a1]';
- P* W8 [! I( `' T
B=[b0 b1]';; R; S\" P( X b$ C) }
format long4 Z4 k; t. i) } Y J
data_out=[A B c' f' kesai_k']# u' o* C1 O/ N9 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：7 N, t, g( G* V
0.0905
\" \/ ?7 M! U- y4 h
$ I2 M# ~ q0 c: W- I& \
迭代次数：
+ C, R, }4 }. f0 H
100次
: x. V\" z2 V+ Z( o' |/ p
% y1 M' f& q E- d( l\" q# m
要求误差0.005000
, z, }1 [* |% P9 L
$ \% \! s9 g$ }# w: v1 C
输出矩阵为：' }' i1 W0 P# R8 F6 j
* x6 S: {& [3 j: e$ n
data_out =' C! O# P& Q5 ?% v, l& e8 w
; A\" ]$ q) H! }5 C; }; r
0 1.000000000000000 0.500000000000000 4.648721270700128 0.500000000000000
# w) j/ {) J4 G8 @* K
0 0.500000000000000 0.250000000000000 1.784025416687741 0.250000000000000
9 v: x* y# W0 q% H r/ J V1 G
0 0.250000000000000 0.125000000000000 0.383148453066826 0.125000000000000* ?1 w1 z6 {9 E\" M1 b7 x9 d2 k
0 0.125000000000000 0.062500000000000 -0.310505541082140 0.062500000000000; z& n; Q/ n# o
0.062500000000000 0.125000000000000 0.093750000000000 0.035785140307826 0.031250000000000, T' X! _6 H3 r6 n+ E, f0 h( b/ }- x
0.062500000000000 0.093750000000000 0.078125000000000 -0.137492192550960 0.015625000000000
\" i7 t. O; p! }: ?5 K7 m
0.078125000000000 0.093750000000000 0.085937500000000 -0.050886782461907 0.007812500000000$ Y8 @# S* W* ~\" y$ @
0.085937500000000 0.093750000000000 0.089843750000000 -0.007559167670695 0.003906250000000
4 ]5 m7 F/ O3 C2 |) i$ ?+ y: \
0.089843750000000 0.093750000000000 0.091796875000000 0.014110895592678 0.001953125000000
0 q2 ~& g: y( I- }
0.089843750000000 0.091796875000000 0.090820312500000 0.003275341789827 0.000976562500000
3 ~. V. S. n) V8 @. j) \
0.089843750000000 0.090820312500000 0.090332031250000 -0.002142043419492 0.000488281250000
) I# w8 e$ L3 Z
0.090332031250000 0.090820312500000 0.090576171875000 0.000566616557439 0.000244140625000
8 m1 k! j, D1 y7 n, B8 |
0.090332031250000 0.090576171875000 0.090454101562500 -0.000787721586963 0.000122070312500
$ }; _: p, S% K4 F: O
0.090454101562500 0.090576171875000 0.090515136718750 -0.000110554553871 0.000061035156250) M G1 e4 F; d! K) Z: a3 T
0.090515136718750 0.090576171875000 0.090545654296875 0.000228030491991 0.000030517578125
2 q) `+ @6 y. J; E+ u
0.090515136718750 0.090545654296875 0.090530395507813 0.000058737841614 0.0000152587890635 l; {+ S9 c* p5 D9 T
0.090515136718750 0.090530395507813 0.090522766113281 -0.000025908387990 0.000007629394531, u\" S' D, |# I7 l$ |2 [
0.090522766113281 0.090530395507813 0.090526580810547 0.000016414718847 0.000003814697266
: o\" |' u, T$ {( @& y( F\" S4 E4 L$ D
0.090522766113281 0.090526580810547 0.090524673461914 -0.000004746836563 0.0000019073486330 w6 J9 U3 B0 H! o/ l
0.090524673461914 0.090526580810547 0.090525627136230 0.000005833940644 0.000000953674316
6 G- P, n& p# B j
0.090524673461914 0.090525627136230 0.090525150299072 0.000000543551916 0.000000476837158+ d: G D( i( a1 D' f' L8 r
0.090524673461914 0.090525150299072 0.090524911880493 -0.000002101642354 0.0000002384185793 S% Q$ N9 X9 Z) Y5 _
0.090524911880493 0.090525150299072 0.090525031089783 -0.000000779045227 0.000000119209290
, {# Z7 c5 ]\" X! S# ~4 O$ u' F
0.090525031089783 0.090525150299072 0.090525090694427 -0.000000117746657 0.000000059604645- g# G5 e; V8 V7 i. O- {/ v
0.090525090694427 0.090525150299072 0.090525120496750 0.000000212902629 0.000000029802322
; ^ H; w7 g3 q& \8 H. e
0.090525090694427 0.090525120496750 0.090525105595589 0.000000047577986 0.000000014901161
- i) i# N0 v* z) |. C+ m
0.090525090694427 0.090525105595589 0.090525098145008 -0.000000035084336 0.000000007450581\" I0 D+ x; X4 k- `) X! z
0.090525098145008 0.090525105595589 0.090525101870298 0.000000006246825 0.000000003725290, w8 |+ u( E- }% l+ T {
0.090525098145008 0.090525101870298 0.090525100007653 -0.000000014418755 0.000000001862645
$ m- I9 X; a+ A Z
0.090525100007653 0.090525101870298 0.090525100938976 -0.000000004085965 0.0000000009313236 X M( }$ E/ ~: l/ T3 h9 a
0.090525100938976 0.090525101870298 0.090525101404637 0.000000001080430 0.000000000465661
0 H/ a+ q( Y+ E) }
0.090525100938976 0.090525101404637 0.090525101171806 -0.000000001502767 0.000000000232831
% p1 l5 g! {8 x: l6 Q! d, I3 E
0.090525101171806 0.090525101404637 0.090525101288222 -0.000000000211169 0.000000000116415
; C# E, h6 B$ v+ I0 @$ V* E
0.090525101288222 0.090525101404637 0.090525101346429 0.000000000434631 0.000000000058208
* ]; M- h4 y1 Q! l2 A, V9 s% l. A' R
0.090525101288222 0.090525101346429 0.090525101317326 0.000000000111731 0.000000000029104
, S1 m& R0 @ O0 M. K
0.090525101288222 0.090525101317326 0.090525101302774 -0.000000000049719 0.000000000014552
4 g4 T0 `, g0 x- C: Q9 U- G- r
0.090525101302774 0.090525101317326 0.090525101310050 0.000000000031006 0.000000000007276
. V0 |/ F; C% d# O0 c
0.090525101302774 0.090525101310050 0.090525101306412 -0.000000000009357 0.000000000003638
( n$ A$ A3 k Q' ~
0.090525101306412 0.090525101310050 0.090525101308231 0.000000000010825 0.000000000001819% V1 B t1 t0 K% l, H
0.090525101306412 0.090525101308231 0.090525101307321 0.000000000000734 0.000000000000909
3 m- h2 r8 b# J
0.090525101306412 0.090525101307321 0.090525101306866 -0.000000000004311 0.000000000000455
- c5 s- e. F1 _
0.090525101306866 0.090525101307321 0.090525101307094 -0.000000000001789 0.000000000000227
/ S1 a. k; i% \$ F5 R: E
0.090525101307094 0.090525101307321 0.090525101307207 -0.000000000000527 0.000000000000114\" L; M S' o, L
0.090525101307207 0.090525101307321 0.090525101307264 0.000000000000103 0.000000000000057
+ f5 l% ^* i9 Q# q; A
0.090525101307207 0.090525101307264 0.090525101307236 -0.000000000000212 0.000000000000028
2 S+ m- _; M' c, C6 a
0.090525101307236 0.090525101307264 0.090525101307250 -0.000000000000054 0.000000000000014
6 w4 L# n {& G' v! X0 Q
0.090525101307250 0.090525101307264 0.090525101307257 0.000000000000025 0.0000000000000074 K8 X; E: @% O+ e, }. u4 f$ J
0.090525101307250 0.090525101307257 0.090525101307254 -0.000000000000015 0.000000000000004
- [4 d, F3 Y, f9 x4 i; N\" V\" b
0.090525101307254 0.090525101307257 0.090525101307255 0.000000000000005 0.000000000000002- Q- A1 w8 E, I2 h! f
0.090525101307254 0.090525101307255 0.090525101307255 -0.000000000000005 0.000000000000001! G6 Y7 j f7 u, V1 s
0.090525101307255 0.090525101307255 0.090525101307255 0 0.000000000000000