[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
: f: t# [\" Z0 v
% n=input('请输入迭代次数：');: p, `/ W$ i& Z* Q- j4 M* V
% qujian=input('请输入初始区间：');
( _7 [9 e& M9 @4 H# [7 v
n=100;- P! h5 \. y# ^6 |: H
wucha=0.005;
, ~1 k: k7 N: X1 y
qujian=[0 1];- ~\" E4 x2 ]1 n. J% C
a(1)=qujian(1);( [2 W7 h* l7 \* x
b(1)=qujian(2);
! ~! O h2 g. l
a0=a(1);
) F9 h( u/ i8 A% Y1 m$ H7 Y+ N2 `
b0=b(1);
1 A B5 i4 _7 P; J% P& c
x=qujian;
& Z+ H- Q+ w5 U: \; {
y=exp(x)+10*x-2;
V4 n1 q# \& ^6 r6 h! P
y1=y(1); %小于0) W. f+ y6 u1 t) y: M( J& C
y2=y(2); %大于0
n$ g' n1 _2 V. q4 M, h5 l
for i=1:n %总迭代次数
+ f! d* X I8 _1 k
c(i)=(a+b)/2;
. m4 ^# f( I! l1 ?7 g: r9 R
f(i)=exp(c(i))+10*(c(i))-2;# _1 O: B* l& ]0 C$ h( R! [# b0 s
kesai_k(i)=(b-a)/2;+ t# v' h) K! m+ s, [
if f(i)>0
# b\" g\" x0 V, a9 ]\" B' N' Z, Y4 }% K
b=c(i);
3 {& }/ B# h7 a2 Z5 H
b1(i)=c(i);( }, V5 P4 M8 t. A7 G& j% Z C
a1(i)=a;
( Y\" p* s, E- `# |/ O& z
elseif f(i)<0) J& z( r( H& N8 n3 ], I( ]* U) r
a=c(i);3 k5 W\" b$ r8 Z. N6 d. ^
a1(i)=c(i);* x. i4 {9 j1 d: L# S' M: p
b1(i)=b;
3 d7 ~\" ^( J8 [; Q1 r
elseif f(i)==0||kesai_k(i)<=wucha
! A/ e: t, ~+ a; ^
disp('精确值解为：');
5 W& N% }* ~: O8 D' p( D7 Y/ \
disp(c(i));1 L* l$ _% F* @# Q
break;4 i _- ]0 p- x+ Z6 l& Q. f
end
; H z0 N n& J
end) Q$ V. u$ F, W
disp('迭代次数：');8 `( q) a; p. J* s j# ?1 R3 E
fprintf('%d次\n\n',n);; j+ M1 K! m- }2 k/ D7 k, h# a
fprintf('要求误差%f\n\n',wucha);+ L# m% ?! z/ B9 y
disp('输出矩阵为：');
9 I4 ^& J0 w( ^( Y9 ?1 Q0 L8 F
A=[a0 a1]';- g, R% t% o$ L) q- k% e: ~
B=[b0 b1]';
V3 m* w+ d {' Y
format long
% v) o8 c' P! ]# y e Z
data_out=[A B c' f' kesai_k']
/ }. [ c+ X/ d
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：
# q4 F+ m( ^2 m. u
0.0905
?( _5 g, P! F4 |% m3 _
\" e, ]6 g+ f% v. S6 z! {+ u
迭代次数：* o4 n. r: B! s& p: q6 E
100次
; D\" G# b; w+ m6 o
! O, p' t$ K% G) }
要求误差0.0050001 C! y+ Q: n4 @# Q' G. g( Y
6 V. |: `; W4 L6 B+ [
输出矩阵为：
) }3 O/ | i8 }6 V- g% }7 ]6 P\" u+ g
& k& @& N4 b& V+ e( C$ }
data_out =$ a1 G\" M5 T3 \! r* o2 n
* E$ Z0 b! x+ a. e6 `3 D5 o6 a
0 1.000000000000000 0.500000000000000 4.648721270700128 0.500000000000000
2 E& W2 r# Y0 @- e) r: {& X* @
0 0.500000000000000 0.250000000000000 1.784025416687741 0.2500000000000009 z1 K1 \. D/ N B; p9 _
0 0.250000000000000 0.125000000000000 0.383148453066826 0.125000000000000/ X( N3 C3 c) M/ U9 r7 Z
0 0.125000000000000 0.062500000000000 -0.310505541082140 0.062500000000000: }6 M2 O: ]' @; U
0.062500000000000 0.125000000000000 0.093750000000000 0.035785140307826 0.031250000000000
; n: V\" @2 {& B# R4 s& K+ ?, t5 v
0.062500000000000 0.093750000000000 0.078125000000000 -0.137492192550960 0.015625000000000( {& o: \0 l5 H7 A8 ?; K
0.078125000000000 0.093750000000000 0.085937500000000 -0.050886782461907 0.0078125000000008 P, S. x2 _8 k7 B' d' |) x
0.085937500000000 0.093750000000000 0.089843750000000 -0.007559167670695 0.003906250000000, P: i9 G, H& H! h' G p
0.089843750000000 0.093750000000000 0.091796875000000 0.014110895592678 0.001953125000000
\" y9 V- _# a. O6 k N1 l+ {
0.089843750000000 0.091796875000000 0.090820312500000 0.003275341789827 0.000976562500000
0 ~0 Z9 U$ p/ Q/ c l7 W4 J
0.089843750000000 0.090820312500000 0.090332031250000 -0.002142043419492 0.000488281250000
( ]6 J4 P$ z2 [\" X9 \
0.090332031250000 0.090820312500000 0.090576171875000 0.000566616557439 0.0002441406250005 p( D' x\" |: J. s2 P8 z3 |9 g
0.090332031250000 0.090576171875000 0.090454101562500 -0.000787721586963 0.000122070312500\" m: {/ s4 J8 Y! O
0.090454101562500 0.090576171875000 0.090515136718750 -0.000110554553871 0.000061035156250- [: c# L [9 Z
0.090515136718750 0.090576171875000 0.090545654296875 0.000228030491991 0.000030517578125
. Y: [# @6 `% n+ W5 h6 o! \
0.090515136718750 0.090545654296875 0.090530395507813 0.000058737841614 0.0000152587890633 x+ e3 e4 w( ]/ P( N. v6 t
0.090515136718750 0.090530395507813 0.090522766113281 -0.000025908387990 0.000007629394531
/ N u, s9 R# \; w
0.090522766113281 0.090530395507813 0.090526580810547 0.000016414718847 0.0000038146972666 O2 l, t/ ?8 k- E2 Y$ _
0.090522766113281 0.090526580810547 0.090524673461914 -0.000004746836563 0.000001907348633$ H5 ^; M; O9 I3 _ e) F6 u' D
0.090524673461914 0.090526580810547 0.090525627136230 0.000005833940644 0.000000953674316( O2 S- k6 E; Z! J
0.090524673461914 0.090525627136230 0.090525150299072 0.000000543551916 0.000000476837158. I; ?2 q/ N, J& ~: p\" [% o5 Q6 b9 K2 b
0.090524673461914 0.090525150299072 0.090524911880493 -0.000002101642354 0.000000238418579
& M$ ]: _. t5 I3 O9 g
0.090524911880493 0.090525150299072 0.090525031089783 -0.000000779045227 0.000000119209290
g+ X+ A7 T! y) P\" L2 @' q
0.090525031089783 0.090525150299072 0.090525090694427 -0.000000117746657 0.000000059604645' Z$ Z$ t4 g4 n& V5 a* I) g
0.090525090694427 0.090525150299072 0.090525120496750 0.000000212902629 0.000000029802322
5 L; g4 n' V0 [5 \5 E9 {: S
0.090525090694427 0.090525120496750 0.090525105595589 0.000000047577986 0.000000014901161
+ n s1 z2 g! d% ]6 { S
0.090525090694427 0.090525105595589 0.090525098145008 -0.000000035084336 0.000000007450581
5 b/ F* B$ c/ O; O) I# f
0.090525098145008 0.090525105595589 0.090525101870298 0.000000006246825 0.000000003725290
6 ]0 B5 p- i. R& L5 X. O, R
0.090525098145008 0.090525101870298 0.090525100007653 -0.000000014418755 0.000000001862645! z6 F8 j5 D9 ^& k
0.090525100007653 0.090525101870298 0.090525100938976 -0.000000004085965 0.000000000931323( B. |+ _! Q8 V. [
0.090525100938976 0.090525101870298 0.090525101404637 0.000000001080430 0.000000000465661
: q$ `8 r9 o# v. c% s7 {
0.090525100938976 0.090525101404637 0.090525101171806 -0.000000001502767 0.0000000002328317 W7 m3 g; N' Y' z
0.090525101171806 0.090525101404637 0.090525101288222 -0.000000000211169 0.000000000116415; N* w+ h0 k, t
0.090525101288222 0.090525101404637 0.090525101346429 0.000000000434631 0.000000000058208
+ Z4 H) C3 S4 ~% n$ J
0.090525101288222 0.090525101346429 0.090525101317326 0.000000000111731 0.000000000029104& t: I9 b% E3 s) L* J9 \9 f5 k
0.090525101288222 0.090525101317326 0.090525101302774 -0.000000000049719 0.000000000014552: x- g/ n. B) S8 W
0.090525101302774 0.090525101317326 0.090525101310050 0.000000000031006 0.000000000007276
0 v/ n( ?8 W4 o\" n3 S
0.090525101302774 0.090525101310050 0.090525101306412 -0.000000000009357 0.0000000000036386 j5 @1 t. B% o4 ~! k4 L
0.090525101306412 0.090525101310050 0.090525101308231 0.000000000010825 0.000000000001819
/ {( Z, }( ^$ \* @! k. L8 u: y! N
0.090525101306412 0.090525101308231 0.090525101307321 0.000000000000734 0.0000000000009091 G# U& F2 y! V7 d4 |& q
0.090525101306412 0.090525101307321 0.090525101306866 -0.000000000004311 0.000000000000455) e* u1 a3 J5 |- H9 r
0.090525101306866 0.090525101307321 0.090525101307094 -0.000000000001789 0.000000000000227
/ p6 l) R7 M7 ] G- r4 R
0.090525101307094 0.090525101307321 0.090525101307207 -0.000000000000527 0.000000000000114
0 j2 l7 S\" [5 S' ^) ^1 |
0.090525101307207 0.090525101307321 0.090525101307264 0.000000000000103 0.000000000000057: R+ C0 ~& d0 n: d; X+ V
0.090525101307207 0.090525101307264 0.090525101307236 -0.000000000000212 0.000000000000028# D) V% [2 }. L' a+ I% y
0.090525101307236 0.090525101307264 0.090525101307250 -0.000000000000054 0.000000000000014
$ T+ f9 c8 e- a4 L& [
0.090525101307250 0.090525101307264 0.090525101307257 0.000000000000025 0.000000000000007% ^/ x3 ]6 q4 m/ v7 O6 I. @) x
0.090525101307250 0.090525101307257 0.090525101307254 -0.000000000000015 0.000000000000004
7 X! T9 W1 V. s9 T- ]% D6 e' B$ s
0.090525101307254 0.090525101307257 0.090525101307255 0.000000000000005 0.000000000000002 U+ s: b* F& `$ |\" d
0.090525101307254 0.090525101307255 0.090525101307255 -0.000000000000005 0.000000000000001
8 `9 D\" ?) w& w$ D0 Q# }$ f+ [5 J
0.090525101307255 0.090525101307255 0.090525101307255 0 0.000000000000000