[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;close3 h- s6 k- D# j. a/ g# |& o
% n=input('请输入迭代次数：'); T. F7 `4 s! f& L! ^( |2 k
% qujian=input('请输入初始区间：');& D( O* x) J5 I) Q5 M
n=100;# g. s- z Z$ R; x$ D( Z; \9 |
wucha=0.005;# S\" \$ Q7 `' ^# C
qujian=[0 1];: j3 @$ i6 b6 V
a(1)=qujian(1);
. [+ \\" m\" N9 h\" y
b(1)=qujian(2); 0 l* i4 X' k& u3 A W7 [6 i5 a! E
a0=a(1);
& E0 T; k3 |1 T* z5 \ D: r
b0=b(1);9 @% L4 Q; W$ {: S6 h! I
x=qujian;1 B$ K* R1 s; T1 I
y=exp(x)+10*x-2;/ b5 g' o, }: e4 E1 @) r/ Q
y1=y(1); %小于0
6 v x; l `# L# h! I) m& {, N
y2=y(2); %大于0
\" @5 @7 X! B0 A2 \. H
for i=1:n %总迭代次数
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c(i)=(a+b)/2;
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f(i)=exp(c(i))+10*(c(i))-2;
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kesai_k(i)=(b-a)/2;\" ~, S+ Z* F2 A1 Z, k& R
if f(i)>0
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b=c(i);\" a( F6 ]- A6 h7 [! Y$ G
b1(i)=c(i);$ Q( a( ?+ \( g( {. ^( A3 q
a1(i)=a;8 R/ @% w4 W! ?: E ~
elseif f(i)<0
v. u* `1 W5 P% Y
a=c(i);
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a1(i)=c(i);+ @4 }) [: r- [+ o8 m
b1(i)=b;3 i3 d# l9 i: J! Q, [- V9 J
elseif f(i)==0||kesai_k(i)<=wucha
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disp('精确值解为：');* t' g) V+ f% v' O4 \' E7 S
disp(c(i));
+ q4 d V z( v8 H1 p# z
break;% p# N: o4 {& J, H1 Q1 n0 {7 _/ r
end0 \* Q/ ?9 C: r\" s; n& H
end
# I2 C4 x9 h! q: r7 @
disp('迭代次数：');
* f3 }. F7 L1 |! S2 ]6 m
fprintf('%d次\n\n',n);
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fprintf('要求误差%f\n\n',wucha);
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disp('输出矩阵为：');5 H! f. ^0 G6 i* \% K1 s. }
A=[a0 a1]';
$ O\" G% g- T/ g1 O
B=[b0 b1]';
3 Q\" X, t3 R- d+ @+ Z/ {
format long3 f: J( ^8 |7 O6 W+ E& v* u
data_out=[A B c' f' kesai_k'] p( n q* D# o
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：, H: s6 j3 y4 ~, r
0.0905
u7 ^) X4 w8 A
; G% D/ b4 k2 W) u! T! f
迭代次数：\" C0 ^3 h! l4 u9 p6 q\" b6 L
100次
# \; _0 c! H; c# e B* X
' E8 a) z! K8 C% u1 N+ ?7 r5 h1 D
要求误差0.005000
3 |$ ^$ {# W3 A/ {
. O. \6 O; c6 ?+ o, s( e8 P
输出矩阵为：
; K' h( L5 E& F, C& Z
# c1 ?) X: ?, I% H
data_out =
+ l9 A0 S% \; p5 B9 x3 W( @
: f. B5 l& d, B5 S* b9 A
0 1.000000000000000 0.500000000000000 4.648721270700128 0.500000000000000# P+ N i9 L5 q0 e1 `! l; a8 a5 Q
0 0.500000000000000 0.250000000000000 1.784025416687741 0.250000000000000
6 K& q. B: B, s& @% {# d5 i3 E8 K) G
0 0.250000000000000 0.125000000000000 0.383148453066826 0.125000000000000! K6 U$ o( J6 J
0 0.125000000000000 0.062500000000000 -0.310505541082140 0.062500000000000: i1 B1 s- V7 E( I7 o\" J
0.062500000000000 0.125000000000000 0.093750000000000 0.035785140307826 0.031250000000000
/ g\" X% @6 j' r
0.062500000000000 0.093750000000000 0.078125000000000 -0.137492192550960 0.015625000000000# Y. ~0 _6 ^$ w5 T! @\" U. q! n, R
0.078125000000000 0.093750000000000 0.085937500000000 -0.050886782461907 0.007812500000000
1 q* E3 {# R7 z\" ?/ |; O
0.085937500000000 0.093750000000000 0.089843750000000 -0.007559167670695 0.003906250000000- v; ^0 E! F6 w5 p/ v
0.089843750000000 0.093750000000000 0.091796875000000 0.014110895592678 0.001953125000000
4 p2 j6 D3 [2 o* u+ D1 { ]) G
0.089843750000000 0.091796875000000 0.090820312500000 0.003275341789827 0.000976562500000
5 ` c/ j/ H\" k* X; |
0.089843750000000 0.090820312500000 0.090332031250000 -0.002142043419492 0.000488281250000
2 q/ V- k- D) p3 I+ B2 J. c
0.090332031250000 0.090820312500000 0.090576171875000 0.000566616557439 0.000244140625000
J. }/ a1 r7 ~5 y
0.090332031250000 0.090576171875000 0.090454101562500 -0.000787721586963 0.000122070312500
$ P- \% j' H/ p
0.090454101562500 0.090576171875000 0.090515136718750 -0.000110554553871 0.000061035156250
) V- Z& W$ Z$ Z2 L2 L
0.090515136718750 0.090576171875000 0.090545654296875 0.000228030491991 0.000030517578125
' \# @8 m7 q/ `( n% o
0.090515136718750 0.090545654296875 0.090530395507813 0.000058737841614 0.000015258789063! s2 U6 J/ T4 s0 d7 j
0.090515136718750 0.090530395507813 0.090522766113281 -0.000025908387990 0.0000076293945313 j; W/ X x9 V
0.090522766113281 0.090530395507813 0.090526580810547 0.000016414718847 0.000003814697266( M# f3 B# T7 A$ F; p: m2 V. f! n4 Y
0.090522766113281 0.090526580810547 0.090524673461914 -0.000004746836563 0.000001907348633
0 s: e) ~8 O' X# i+ E
0.090524673461914 0.090526580810547 0.090525627136230 0.000005833940644 0.000000953674316
5 u2 x2 S! p8 ^8 N8 s
0.090524673461914 0.090525627136230 0.090525150299072 0.000000543551916 0.000000476837158
0.090524673461914 0.090525150299072 0.090524911880493 -0.000002101642354 0.0000002384185792 r9 @/ P7 i3 M% o
0.090524911880493 0.090525150299072 0.090525031089783 -0.000000779045227 0.000000119209290& T! P1 Y; w/ o; y7 L; W
0.090525031089783 0.090525150299072 0.090525090694427 -0.000000117746657 0.000000059604645) n- U2 C0 d j5 {
0.090525090694427 0.090525150299072 0.090525120496750 0.000000212902629 0.000000029802322
% f/ a s4 D2 s( z/ M\" D
0.090525090694427 0.090525120496750 0.090525105595589 0.000000047577986 0.000000014901161
e. O9 n; L4 O: t# y' @$ Q
0.090525090694427 0.090525105595589 0.090525098145008 -0.000000035084336 0.000000007450581% o$ h/ n2 H) z3 i+ m
0.090525098145008 0.090525105595589 0.090525101870298 0.000000006246825 0.000000003725290' x; R% {1 l( Q
0.090525098145008 0.090525101870298 0.090525100007653 -0.000000014418755 0.000000001862645
( H! l2 ~- x5 e8 b
0.090525100007653 0.090525101870298 0.090525100938976 -0.000000004085965 0.000000000931323+ @, ]- q7 R5 N. H8 ]+ m\" P! a\" ~
0.090525100938976 0.090525101870298 0.090525101404637 0.000000001080430 0.000000000465661
9 \& c, P: l& }. t9 ?# k
0.090525100938976 0.090525101404637 0.090525101171806 -0.000000001502767 0.000000000232831/ F5 }$ {: b! N8 W
0.090525101171806 0.090525101404637 0.090525101288222 -0.000000000211169 0.000000000116415
3 }! X: V1 e2 p9 Z
0.090525101288222 0.090525101404637 0.090525101346429 0.000000000434631 0.000000000058208
& e9 r2 L$ E* C\" g% K
0.090525101288222 0.090525101346429 0.090525101317326 0.000000000111731 0.0000000000291048 `: M. @& T* O. K' F2 w6 l- [
0.090525101288222 0.090525101317326 0.090525101302774 -0.000000000049719 0.000000000014552. ?8 r6 w( p- l& Z$ I/ w! i& a% Q
0.090525101302774 0.090525101317326 0.090525101310050 0.000000000031006 0.000000000007276
$ W% T- T\" ^2 h, Q+ C- F
0.090525101302774 0.090525101310050 0.090525101306412 -0.000000000009357 0.0000000000036386 R\" U( T\" t6 d7 q
0.090525101306412 0.090525101310050 0.090525101308231 0.000000000010825 0.000000000001819
t5 b. C }/ G$ {0 Z! i
0.090525101306412 0.090525101308231 0.090525101307321 0.000000000000734 0.000000000000909' L5 R8 y9 v+ K5 B) R3 g: S
0.090525101306412 0.090525101307321 0.090525101306866 -0.000000000004311 0.000000000000455- S- q( b) A8 E3 R
0.090525101306866 0.090525101307321 0.090525101307094 -0.000000000001789 0.000000000000227) Y! u' @\" T# @' N
0.090525101307094 0.090525101307321 0.090525101307207 -0.000000000000527 0.0000000000001147 b5 b; H& P' c; f) h! E* D6 G
0.090525101307207 0.090525101307321 0.090525101307264 0.000000000000103 0.000000000000057
7 o% Q- k\" d; Z. N( D
0.090525101307207 0.090525101307264 0.090525101307236 -0.000000000000212 0.0000000000000289 a# v( F/ ~. y5 g6 I0 K4 u0 V
0.090525101307236 0.090525101307264 0.090525101307250 -0.000000000000054 0.0000000000000148 [: Q+ w& L& x& h% \8 e o& h; D\" q
0.090525101307250 0.090525101307264 0.090525101307257 0.000000000000025 0.000000000000007& U9 p d4 L3 [9 A
0.090525101307250 0.090525101307257 0.090525101307254 -0.000000000000015 0.000000000000004
\" _: \: Y/ x\" @6 r5 ^% S4 @
0.090525101307254 0.090525101307257 0.090525101307255 0.000000000000005 0.000000000000002
' P, U6 y; b5 s$ X# E! T
0.090525101307254 0.090525101307255 0.090525101307255 -0.000000000000005 0.000000000000001
+ P* M m8 k$ J0 N! j) }. W# O3 _
0.090525101307255 0.090525101307255 0.090525101307255 0 0.000000000000000