[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 |正序浏览

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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
( K/ i/ `9 S5 {0 `
% n=input('请输入迭代次数：');
% N; M: ~0 m5 k% A3 s
% qujian=input('请输入初始区间：');
- s |4 w6 I4 R2 E
n=100;
$ J! X* ?9 A/ r4 i$ I9 v
wucha=0.005;3 V: \4 i) e2 W$ w# P; v
qujian=[0 1];! s. \/ w4 Z0 P& P' l: Z
a(1)=qujian(1);; w- _% G; z$ }5 }$ t6 |
b(1)=qujian(2); \" P! e4 V2 R9 o- P& D! G
a0=a(1);! L0 |- \( b4 h7 n
b0=b(1);
4 l: R2 f0 i$ y4 w
x=qujian;\" Q8 O Y, d' ]
y=exp(x)+10*x-2;
4 Q: V# ~6 V# l# y\" k9 v
y1=y(1); %小于0
! o4 c# d4 G! \' X' N
y2=y(2); %大于0
a% H, C\" D/ E2 y2 \: P1 j
for i=1:n %总迭代次数
* r9 G4 b0 K* \8 D# e4 R
c(i)=(a+b)/2;% j9 r! U$ B' A
f(i)=exp(c(i))+10*(c(i))-2;3 j4 H, u) k% Y1 I
kesai_k(i)=(b-a)/2;
) E8 F/ [2 l4 p# j$ g
if f(i)>0
5 |2 t! Z( m( U0 {, W
b=c(i);
\" ~2 T+ |& e' M+ R
b1(i)=c(i);& I) `; c; [: R- v2 H+ k+ L
a1(i)=a;
$ Z& m1 d' F% S) k! H- r
elseif f(i)<0' X8 |3 C! e4 \* |. F
a=c(i);& H+ u* C, |6 c' Y2 E+ D5 V/ W
a1(i)=c(i);. |\" _4 ~+ o& x/ p
b1(i)=b;- [# ?0 K7 S8 o6 S/ Y5 x5 w% B
elseif f(i)==0||kesai_k(i)<=wucha
5 v# t- z8 y+ d, D/ T% Y
disp('精确值解为：');( s7 E8 l& z5 d: X8 U
disp(c(i));3 j5 |0 }8 e. g$ F4 J# v\" ^( C
break;
8 b$ @\" c; A5 c) n
end0 a! m$ b! Z; c K: y
end
( H. w' `% q9 [2 h\" J: B
disp('迭代次数：');
- Q% A& Y9 b3 i. w' Y
fprintf('%d次\n\n',n);* ]9 y0 P5 u) `
fprintf('要求误差%f\n\n',wucha);- x) X$ {2 g6 t% S3 _- H# u3 R
disp('输出矩阵为：');
) a1 b9 O& s$ [) W( A: v
A=[a0 a1]';
$ s# H& M, t+ C( r' b) T4 v% |\" `
B=[b0 b1]';$ a2 P, {: @( }' I, j( c- o
format long
3 ~. l1 Z* u/ {4 S
data_out=[A B c' f' kesai_k']8 }6 P7 C, p7 y9 ~- H
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：
% M) q- ]8 l# n\" G8 O
0.0905+ `) z. g. J) V8 P* z
\" i, |$ ]7 l+ L5 p' ?
迭代次数：8 I\" r: W9 e- Y6 h1 D9 n9 O
100次/ R: C+ X( h- D4 l9 Z2 Z5 U
9 ~1 ~5 T9 A: B2 c( B8 g2 w6 g
要求误差0.005000
w! g: T6 K% x' r; B
* a6 @: h! G' q8 w
输出矩阵为：3 d2 q7 M4 ]& B/ z/ O; u
6 \( ]% ?2 e6 u
data_out =, I n\" e\" q% \: b: p
) Y+ q# {8 R' l8 o2 ]3 N9 r& g
0 1.000000000000000 0.500000000000000 4.648721270700128 0.5000000000000006 p( |) p( Q8 R( x* x0 }1 a
0 0.500000000000000 0.250000000000000 1.784025416687741 0.250000000000000
7 ^+ h' M' {! o! R6 _1 o- g
0 0.250000000000000 0.125000000000000 0.383148453066826 0.125000000000000
, i/ n/ M3 K) E6 F: Z3 p) ^' o( a5 ]5 T
0 0.125000000000000 0.062500000000000 -0.310505541082140 0.062500000000000
9 u& b: S6 C/ H. y4 G* p2 E m
0.062500000000000 0.125000000000000 0.093750000000000 0.035785140307826 0.031250000000000
: Q9 r. ?% o7 \- f! ^
0.062500000000000 0.093750000000000 0.078125000000000 -0.137492192550960 0.015625000000000
2 W2 x8 S, E1 E- z6 O2 l0 g
0.078125000000000 0.093750000000000 0.085937500000000 -0.050886782461907 0.0078125000000008 h, F4 t\" @/ X' Z. G& ~# D, h
0.085937500000000 0.093750000000000 0.089843750000000 -0.007559167670695 0.003906250000000
; a! c* d; W* e- t
0.089843750000000 0.093750000000000 0.091796875000000 0.014110895592678 0.001953125000000% D& b) `3 F8 a. {7 G3 Q6 h
0.089843750000000 0.091796875000000 0.090820312500000 0.003275341789827 0.000976562500000* b* s- T9 z$ K% H m
0.089843750000000 0.090820312500000 0.090332031250000 -0.002142043419492 0.000488281250000
7 e4 U% ^$ y8 V
0.090332031250000 0.090820312500000 0.090576171875000 0.000566616557439 0.000244140625000 f% a4 ^9 c+ N3 E* f! g
0.090332031250000 0.090576171875000 0.090454101562500 -0.000787721586963 0.0001220703125005 [$ l) k\" N/ g' M- J
0.090454101562500 0.090576171875000 0.090515136718750 -0.000110554553871 0.000061035156250
: O; x& R\" |' p% g3 } n- O: y4 P
0.090515136718750 0.090576171875000 0.090545654296875 0.000228030491991 0.000030517578125% S Z V/ }/ ^$ o) D\" W% l' V
0.090515136718750 0.090545654296875 0.090530395507813 0.000058737841614 0.000015258789063
+ y6 w' n( t% i, S\" j
0.090515136718750 0.090530395507813 0.090522766113281 -0.000025908387990 0.000007629394531\" r' k* [0 ^4 m7 m [( n+ M
0.090522766113281 0.090530395507813 0.090526580810547 0.000016414718847 0.000003814697266
X( j9 `, Z& P
0.090522766113281 0.090526580810547 0.090524673461914 -0.000004746836563 0.000001907348633
6 l$ ^\" x$ a4 w% a
0.090524673461914 0.090526580810547 0.090525627136230 0.000005833940644 0.0000009536743162 {2 s$ R8 g: o6 U* n. F
0.090524673461914 0.090525627136230 0.090525150299072 0.000000543551916 0.000000476837158
9 u( [. b x2 U% C( k
0.090524673461914 0.090525150299072 0.090524911880493 -0.000002101642354 0.000000238418579
3 a( W+ p3 @3 i\" u8 J* v- q
0.090524911880493 0.090525150299072 0.090525031089783 -0.000000779045227 0.000000119209290
1 k7 X6 ]+ n9 M% [9 ^- [
0.090525031089783 0.090525150299072 0.090525090694427 -0.000000117746657 0.000000059604645) s9 c- p: j2 w. [* b$ s7 q
0.090525090694427 0.090525150299072 0.090525120496750 0.000000212902629 0.000000029802322# w! o) a, k1 c4 c5 F( U& z& U0 f2 D) Q
0.090525090694427 0.090525120496750 0.090525105595589 0.000000047577986 0.000000014901161
9 H2 l) u5 ^, Q9 P: k3 Y, W
0.090525090694427 0.090525105595589 0.090525098145008 -0.000000035084336 0.000000007450581
( c# k( u2 e2 ~
0.090525098145008 0.090525105595589 0.090525101870298 0.000000006246825 0.0000000037252902 L4 v+ D8 f) c+ Y5 e6 M
0.090525098145008 0.090525101870298 0.090525100007653 -0.000000014418755 0.000000001862645
- p5 h; x! e* }$ M, p% g
0.090525100007653 0.090525101870298 0.090525100938976 -0.000000004085965 0.000000000931323- c/ f1 R, r\" _8 Q
0.090525100938976 0.090525101870298 0.090525101404637 0.000000001080430 0.0000000004656618 B0 p# a6 e: }, L
0.090525100938976 0.090525101404637 0.090525101171806 -0.000000001502767 0.000000000232831
8 l7 Y9 E9 W B5 k: W, q
0.090525101171806 0.090525101404637 0.090525101288222 -0.000000000211169 0.0000000001164158 v, b9 E3 ]( l; P\" Q
0.090525101288222 0.090525101404637 0.090525101346429 0.000000000434631 0.000000000058208
6 X& y$ M) R! D$ _0 H
0.090525101288222 0.090525101346429 0.090525101317326 0.000000000111731 0.0000000000291047 H$ r; r( Y8 P2 Y7 i) F
0.090525101288222 0.090525101317326 0.090525101302774 -0.000000000049719 0.000000000014552
! y5 w) p4 {. C6 H5 k
0.090525101302774 0.090525101317326 0.090525101310050 0.000000000031006 0.000000000007276* ^* m) {% c( u- R0 b- I8 a
0.090525101302774 0.090525101310050 0.090525101306412 -0.000000000009357 0.000000000003638
. n\" f* R3 o; W5 F4 E; i: ?
0.090525101306412 0.090525101310050 0.090525101308231 0.000000000010825 0.000000000001819
4 ?2 Z3 D4 ]; `: ?
0.090525101306412 0.090525101308231 0.090525101307321 0.000000000000734 0.000000000000909 L6 `; G! K( D, o! V9 J
0.090525101306412 0.090525101307321 0.090525101306866 -0.000000000004311 0.000000000000455$ H! `0 v# m& @
0.090525101306866 0.090525101307321 0.090525101307094 -0.000000000001789 0.000000000000227
+ q& F9 c1 q2 y
0.090525101307094 0.090525101307321 0.090525101307207 -0.000000000000527 0.0000000000001148 X' C& \+ b5 d4 F4 E
0.090525101307207 0.090525101307321 0.090525101307264 0.000000000000103 0.0000000000000570 b7 _! r0 M- _
0.090525101307207 0.090525101307264 0.090525101307236 -0.000000000000212 0.000000000000028
1 R% w& [3 N' G( k* e0 ^\" ]% ^4 T
0.090525101307236 0.090525101307264 0.090525101307250 -0.000000000000054 0.0000000000000148 z- k ~. O# {1 X4 C
0.090525101307250 0.090525101307264 0.090525101307257 0.000000000000025 0.0000000000000070 [) y' j$ n+ J. w) K O
0.090525101307250 0.090525101307257 0.090525101307254 -0.000000000000015 0.000000000000004
! p* \, ?; L$ F
0.090525101307254 0.090525101307257 0.090525101307255 0.000000000000005 0.000000000000002) P, u/ t' ~; B: {5 {
0.090525101307254 0.090525101307255 0.090525101307255 -0.000000000000005 0.000000000000001
9 k/ t* Q* M\" a+ i; c# K0 n0 K% t
0.090525101307255 0.090525101307255 0.090525101307255 0 0.000000000000000