[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' U- G! h ~2 R\" W8 I
% n=input('请输入迭代次数：');# d$ p ?/ A- D
% qujian=input('请输入初始区间：');
5 y* ]( R+ U4 k
n=100;
4 x( E) L* v1 p( \% g
wucha=0.005;
# R0 j9 G7 @5 Z: b0 H
qujian=[0 1];( L: u5 U; u. N7 I( I6 v% f
a(1)=qujian(1);
9 d& Y( L4 C' p( O- ^
b(1)=qujian(2); / ?' r5 `' }. v& v$ b1 m
a0=a(1);
8 X6 V# H ^* z) g: k* _- h
b0=b(1);4 O# c, o: |5 m; o# v% |
x=qujian;
. G1 }- l' ^( _- q# W* [
y=exp(x)+10*x-2;
- X+ s' B2 ^. h5 o6 e
y1=y(1); %小于0 G& I\" g0 s& X
y2=y(2); %大于0
3 g8 [; Q' b* E
for i=1:n %总迭代次数5 c( K6 w1 `1 N9 `
c(i)=(a+b)/2;
& N$ {) T1 I8 w3 D
f(i)=exp(c(i))+10*(c(i))-2;; t3 U& K! {& g) K\" X/ r5 c
kesai_k(i)=(b-a)/2;
* Q8 ]2 ?6 `9 H$ Z k1 X# H
if f(i)>0
\" h8 d B; }& F# G- Q* B
b=c(i);
) n1 X: e) u: ?
b1(i)=c(i);6 {# `! k\" x* G% z3 @8 P! H
a1(i)=a;
+ s5 v6 r4 d* ]8 I- G# j
elseif f(i)<05 Q( ^. @( U8 o+ r8 E0 ]% n2 ?
a=c(i);
8 J' C4 V- l K7 K: B/ H
a1(i)=c(i);
0 W/ j# I+ r6 S& I+ s6 _
b1(i)=b;& I2 X& m. Q2 S' |
elseif f(i)==0||kesai_k(i)<=wucha( a* @\" j' x/ @; G
disp('精确值解为：');; Q0 f, Z) J! W& D- U! q! a
disp(c(i)); U: |# r6 R! g6 N
break;
* I( n3 m\" z0 F. v
end
7 D% H6 d1 c+ v% {! h
end1 q3 k9 r0 Z% u8 v
disp('迭代次数：');/ u5 f* N) e$ |0 d* t. z) ?
fprintf('%d次\n\n',n);
8 l* L- h7 X, _: K: T
fprintf('要求误差%f\n\n',wucha);4 ?+ O* E6 c+ E: V
disp('输出矩阵为：');2 e* z* m& D* e/ L0 L5 ~$ r, q; [2 v' F
A=[a0 a1]';
# A0 A8 }! F9 Q0 F% Q+ l1 b
B=[b0 b1]';; V! o/ I1 `2 n' P* e
format long
. c, [6 R4 W& u5 |\" o& R
data_out=[A B c' f' kesai_k']) m2 Y, c* w' ?4 `5 u( i8 u
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：( O* K) }: |% s& \0 Y
0.0905
$ Y9 f4 d2 O$ G8 x! m0 U, S& G
- D- i( G2 l2 n# w5 T2 }
迭代次数：
; V# A; A( v0 o9 V9 n5 e, C9 E4 z
100次
: f6 e7 d1 Y8 B
1 T C, {8 W3 o; j: W% C9 M
要求误差0.005000 I- |6 E: {\" [* S: L( q% C) K
5 y7 G9 t$ L% i
输出矩阵为：8 }; ^) `# }$ p$ A2 z) n' r
& ~\" X6 Q! r9 q
data_out =
1 u* j v; P4 u\" D+ n: l! P
6 t6 x# c# d, t8 R( o6 f8 J1 i9 U
0 1.000000000000000 0.500000000000000 4.648721270700128 0.500000000000000
4 c4 w7 r$ T8 R; v9 `+ r
0 0.500000000000000 0.250000000000000 1.784025416687741 0.250000000000000( ~* ?. m, R2 [* ^7 l
0 0.250000000000000 0.125000000000000 0.383148453066826 0.125000000000000
8 `7 t# R% w1 c7 x7 t9 W
0 0.125000000000000 0.062500000000000 -0.310505541082140 0.062500000000000
6 S! H) O9 f, o9 Z
0.062500000000000 0.125000000000000 0.093750000000000 0.035785140307826 0.031250000000000
\" ]) \+ O0 N2 g+ H! W
0.062500000000000 0.093750000000000 0.078125000000000 -0.137492192550960 0.0156250000000007 c7 Q& Y/ f' g. o
0.078125000000000 0.093750000000000 0.085937500000000 -0.050886782461907 0.007812500000000) W/ z1 r0 C# H+ K3 |# g2 S
0.085937500000000 0.093750000000000 0.089843750000000 -0.007559167670695 0.003906250000000
6 _ T% c4 [5 |# y- i t
0.089843750000000 0.093750000000000 0.091796875000000 0.014110895592678 0.001953125000000
+ E( P' G! K7 M# Y) S W
0.089843750000000 0.091796875000000 0.090820312500000 0.003275341789827 0.000976562500000& Z% _# L- T3 P9 b4 H
0.089843750000000 0.090820312500000 0.090332031250000 -0.002142043419492 0.0004882812500008 |: @3 x8 v& p6 [5 ]
0.090332031250000 0.090820312500000 0.090576171875000 0.000566616557439 0.000244140625000
) \1 V3 J6 b, g [4 ~8 ]
0.090332031250000 0.090576171875000 0.090454101562500 -0.000787721586963 0.000122070312500
9 g4 R4 ? F( y
0.090454101562500 0.090576171875000 0.090515136718750 -0.000110554553871 0.000061035156250
* M+ u& R! [: C; D9 X0 A; R, \
0.090515136718750 0.090576171875000 0.090545654296875 0.000228030491991 0.000030517578125. [4 f0 N1 u\" q
0.090515136718750 0.090545654296875 0.090530395507813 0.000058737841614 0.000015258789063
- X- {\" S: q% i5 H, P# \# z
0.090515136718750 0.090530395507813 0.090522766113281 -0.000025908387990 0.000007629394531$ e. f0 Z& X' _! ]- Z7 E
0.090522766113281 0.090530395507813 0.090526580810547 0.000016414718847 0.000003814697266
7 [ B' c\" d% K1 p8 h$ C
0.090522766113281 0.090526580810547 0.090524673461914 -0.000004746836563 0.000001907348633* d$ \; m( n/ c6 W. g+ L
0.090524673461914 0.090526580810547 0.090525627136230 0.000005833940644 0.0000009536743162 ~9 T, P0 _( N' J2 i
0.090524673461914 0.090525627136230 0.090525150299072 0.000000543551916 0.000000476837158
/ }7 H$ x' ]1 u4 @
0.090524673461914 0.090525150299072 0.090524911880493 -0.000002101642354 0.000000238418579: F% ~+ z7 Z6 H( w: g9 n# u
0.090524911880493 0.090525150299072 0.090525031089783 -0.000000779045227 0.000000119209290
' X! N+ N- k) y6 S( L
0.090525031089783 0.090525150299072 0.090525090694427 -0.000000117746657 0.000000059604645, i2 _4 e+ F) o# ]$ y% J( K
0.090525090694427 0.090525150299072 0.090525120496750 0.000000212902629 0.000000029802322
2 O# X& A: Z; |6 V% T
0.090525090694427 0.090525120496750 0.090525105595589 0.000000047577986 0.000000014901161! e$ {: r: d' M
0.090525090694427 0.090525105595589 0.090525098145008 -0.000000035084336 0.0000000074505812 ~; x$ C* f) t! ^2 Q. i
0.090525098145008 0.090525105595589 0.090525101870298 0.000000006246825 0.000000003725290
/ ?. r T/ H4 P) X! F: M6 w% X
0.090525098145008 0.090525101870298 0.090525100007653 -0.000000014418755 0.000000001862645
\" e: Z0 p0 A% x F
0.090525100007653 0.090525101870298 0.090525100938976 -0.000000004085965 0.000000000931323
) W4 q' g1 g+ i
0.090525100938976 0.090525101870298 0.090525101404637 0.000000001080430 0.000000000465661+ W- [6 r V3 X# r- r, ~0 f& j& N% o
0.090525100938976 0.090525101404637 0.090525101171806 -0.000000001502767 0.000000000232831
1 Q2 o8 w2 n9 s {% |- f
0.090525101171806 0.090525101404637 0.090525101288222 -0.000000000211169 0.000000000116415
& R5 f+ Y\" f# g8 G: u
0.090525101288222 0.090525101404637 0.090525101346429 0.000000000434631 0.0000000000582081 Y7 b& g& i+ {9 Z: J1 [2 K. Q% ]
0.090525101288222 0.090525101346429 0.090525101317326 0.000000000111731 0.000000000029104
% P, z; U) T* z! ]- }0 m
0.090525101288222 0.090525101317326 0.090525101302774 -0.000000000049719 0.000000000014552
u& k1 ~ E, x2 [! v9 D2 ], u\" U
0.090525101302774 0.090525101317326 0.090525101310050 0.000000000031006 0.000000000007276
3 M! q1 U# I5 ^7 D
0.090525101302774 0.090525101310050 0.090525101306412 -0.000000000009357 0.000000000003638' ?/ G5 a8 w4 j
0.090525101306412 0.090525101310050 0.090525101308231 0.000000000010825 0.0000000000018199 P9 n- C2 b/ o2 D m
0.090525101306412 0.090525101308231 0.090525101307321 0.000000000000734 0.000000000000909
: \/ B0 m5 L\" l1 j; z& d% u' O
0.090525101306412 0.090525101307321 0.090525101306866 -0.000000000004311 0.0000000000004559 R5 Y0 g# w' s, C% N
0.090525101306866 0.090525101307321 0.090525101307094 -0.000000000001789 0.000000000000227
) w, H z* q! H' R$ ^6 f
0.090525101307094 0.090525101307321 0.090525101307207 -0.000000000000527 0.000000000000114\" T8 ]7 T0 h6 h; w5 Z5 w- c
0.090525101307207 0.090525101307321 0.090525101307264 0.000000000000103 0.000000000000057
& }, v' w. R1 a4 F& h0 Q
0.090525101307207 0.090525101307264 0.090525101307236 -0.000000000000212 0.000000000000028, u% e: k/ _4 L, P1 B V1 w
0.090525101307236 0.090525101307264 0.090525101307250 -0.000000000000054 0.000000000000014
2 F' x\" N7 H\" C2 N* t# n
0.090525101307250 0.090525101307264 0.090525101307257 0.000000000000025 0.000000000000007
4 q& [1 w* [( Z' V, w- l
0.090525101307250 0.090525101307257 0.090525101307254 -0.000000000000015 0.000000000000004+ M6 t+ w2 n1 q6 J8 v q) p1 `; x\" a
0.090525101307254 0.090525101307257 0.090525101307255 0.000000000000005 0.0000000000000024 d. C) c* Z0 Q
0.090525101307254 0.090525101307255 0.090525101307255 -0.000000000000005 0.000000000000001
0 Q1 o6 M. d3 Y; j- Y
0.090525101307255 0.090525101307255 0.090525101307255 0 0.000000000000000