[代码资源] 用对分法解超越方程

[复制链接]

字体大小: 正常放大

seven3069

18 主题	15 听众	945 积分

升级 86.25%

TA的每日心情

	奋斗 2018-11-27 09:23

签到天数: 395 天

[LV.9]以坛为家II

群组: 2016国赛备战群组

电梯直达

1^#

发表于 2016-10-12 23:05 |只看该作者 |倒序浏览

|招呼Ta 关注Ta

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
& e3 |( j3 x+ Y k+ [9 C
% n=input('请输入迭代次数：');2 N0 v5 F) r; x
% qujian=input('请输入初始区间：');$ Q2 w% K/ J6 a! I9 l$ w& j; w
n=100;/ M6 ~# Q4 p0 K8 C# z8 I) ]
wucha=0.005;
- c6 r) `5 Q, D! C( o. G
qujian=[0 1];
6 w4 n/ L7 \9 g. y
a(1)=qujian(1);+ r2 O1 Z\" i2 }. N9 u/ Q k; L
b(1)=qujian(2);
0 u( |/ L' p( J
a0=a(1);0 b2 J8 J1 P# Q; U* W
b0=b(1);( S' n4 w: M) ]% ]
x=qujian;
8 Y( Y: m- X\" G
y=exp(x)+10*x-2;
7 T/ ~1 |! R E2 a9 E& J0 q0 @! W
y1=y(1); %小于0, D# a; ]) ?4 _( a! S
y2=y(2); %大于0
for i=1:n %总迭代次数
9 N: B) K; A\" p4 V) [8 o& h
c(i)=(a+b)/2;
+ M1 k3 j\" m% O% _% W+ i6 T4 j+ q
f(i)=exp(c(i))+10*(c(i))-2;
3 |% B8 t7 W1 P/ I, N
kesai_k(i)=(b-a)/2;0 m# C4 X4 ^$ j0 B7 H
if f(i)>0+ g6 u; y, D1 ~% F9 W
b=c(i);8 J\" j7 h\" e\" D/ n. e% n/ C
b1(i)=c(i);0 M- o2 {\" @3 }4 d
a1(i)=a;
! E% I: [' k% ]) B- C3 h
elseif f(i)<06 s' h6 G9 i# G& G8 u\" l# p
a=c(i);
2 s Q3 Z6 j/ p
a1(i)=c(i);
\" }7 a\" b. `\" ?: B
b1(i)=b;% s. }, U R+ v% M- i# {% j
elseif f(i)==0||kesai_k(i)<=wucha9 D$ L/ ^. U5 a2 T
disp('精确值解为：');& \( _\" O* O' `: M8 ~
disp(c(i));7 X( J% w( @% d6 W8 E( V C. H9 Z, T
break;( R4 ^- f. h6 m$ P9 D
end
7 Q; M! u, X\" l' C, M3 x
end4 A5 x: t6 B' ]' |& s
disp('迭代次数：');
9 h* l( a1 a# z6 t
fprintf('%d次\n\n',n);7 S! {! D7 {! h% \. i: ~* |
fprintf('要求误差%f\n\n',wucha);( y4 M6 ~! m- b* ?7 R! _
disp('输出矩阵为：');9 K$ K0 h( l\" i0 n- E! \7 i: M* X S
A=[a0 a1]';
# ?5 z1 x) I5 ]6 _# ^8 M
B=[b0 b1]';
/ \: }- X7 @' O% g
format long
6 x, ?; }: x% V* l, o\" u
data_out=[A B c' f' kesai_k'], v' f; ^% N, h4 w. s `\" 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：
5 |/ [. y$ s( e; F4 B c\" k$ L
0.0905* f( {3 ~# ^. {\" Y; t6 S- ]/ S
% o0 F& O. u\" r7 F# M- y6 h
迭代次数：5 X1 Y, c0 j. k1 \% `
100次
* H% m\" z w; u+ _\" V5 z4 \! Y
& h0 h0 B' M1 b( f: s/ Y: ?- A
要求误差0.005000
# s. H+ C6 H, \! X3 V
\" o3 N4 p$ {* r9 C: }
输出矩阵为：! D/ P( T. }5 `1 z2 s
: I5 |! |( w1 b P+ v9 M1 t
data_out =* f; U/ a- ~; O5 y: B. D3 Q# G
+ i9 c+ P$ X: H9 F
0 1.000000000000000 0.500000000000000 4.648721270700128 0.500000000000000
: N\" r e- u v
0 0.500000000000000 0.250000000000000 1.784025416687741 0.250000000000000
\" c; y' j5 Z( r& F, H0 a- m, w2 {4 w
0 0.250000000000000 0.125000000000000 0.383148453066826 0.125000000000000
; y2 u- j9 I( k6 L6 ]2 u
0 0.125000000000000 0.062500000000000 -0.310505541082140 0.062500000000000/ g: O4 \+ T0 Z6 r p
0.062500000000000 0.125000000000000 0.093750000000000 0.035785140307826 0.031250000000000: K8 b$ I8 T2 B/ \1 ?$ e
0.062500000000000 0.093750000000000 0.078125000000000 -0.137492192550960 0.015625000000000
/ X: b1 L# F* O8 ?' }9 D
0.078125000000000 0.093750000000000 0.085937500000000 -0.050886782461907 0.0078125000000005 R8 e; d' J/ S+ B, M# d, @
0.085937500000000 0.093750000000000 0.089843750000000 -0.007559167670695 0.003906250000000
~# q& R. q+ U
0.089843750000000 0.093750000000000 0.091796875000000 0.014110895592678 0.001953125000000
% j- z8 F\" C2 F
0.089843750000000 0.091796875000000 0.090820312500000 0.003275341789827 0.000976562500000
* T: H! ^1 U/ F
0.089843750000000 0.090820312500000 0.090332031250000 -0.002142043419492 0.000488281250000
7 L/ D8 p1 x* J( ?2 k
0.090332031250000 0.090820312500000 0.090576171875000 0.000566616557439 0.0002441406250006 Z7 e4 y& P\" K* |0 J
0.090332031250000 0.090576171875000 0.090454101562500 -0.000787721586963 0.000122070312500+ i, Q! e& ~- z: q8 s2 ?4 u, V
0.090454101562500 0.090576171875000 0.090515136718750 -0.000110554553871 0.000061035156250: Y& E% T\" x4 o, Y6 G
0.090515136718750 0.090576171875000 0.090545654296875 0.000228030491991 0.000030517578125* t* M' i6 r' D0 p) a' _
0.090515136718750 0.090545654296875 0.090530395507813 0.000058737841614 0.000015258789063
& A9 K7 G( v. ^* N3 |8 X
0.090515136718750 0.090530395507813 0.090522766113281 -0.000025908387990 0.000007629394531
7 m3 g* G& S d\" z3 n- k* c
0.090522766113281 0.090530395507813 0.090526580810547 0.000016414718847 0.000003814697266
# y3 p ~- ~2 @7 M
0.090522766113281 0.090526580810547 0.090524673461914 -0.000004746836563 0.000001907348633( l4 |+ l. U `4 f& V: s
0.090524673461914 0.090526580810547 0.090525627136230 0.000005833940644 0.000000953674316 q' c3 V$ |2 r: \* e# C9 N) V
0.090524673461914 0.090525627136230 0.090525150299072 0.000000543551916 0.000000476837158
$ u8 p; A7 _* K0 i) B% p4 o# N
0.090524673461914 0.090525150299072 0.090524911880493 -0.000002101642354 0.000000238418579
! Z7 X1 t, h+ r( B5 I; R
0.090524911880493 0.090525150299072 0.090525031089783 -0.000000779045227 0.000000119209290\" D% n; |\" M: U# B0 a' `
0.090525031089783 0.090525150299072 0.090525090694427 -0.000000117746657 0.000000059604645& s\" @5 q0 E# m* z% B3 q) R
0.090525090694427 0.090525150299072 0.090525120496750 0.000000212902629 0.000000029802322
7 `' A5 v4 R( ?5 V: a\" d4 v5 ?
0.090525090694427 0.090525120496750 0.090525105595589 0.000000047577986 0.000000014901161/ V1 r/ Z' K+ ^% u8 {
0.090525090694427 0.090525105595589 0.090525098145008 -0.000000035084336 0.000000007450581\" P\" w' X$ {: P1 v
0.090525098145008 0.090525105595589 0.090525101870298 0.000000006246825 0.000000003725290; v. i, P. W3 z% u7 w\" Z$ O
0.090525098145008 0.090525101870298 0.090525100007653 -0.000000014418755 0.000000001862645, n- E) ?6 u# h
0.090525100007653 0.090525101870298 0.090525100938976 -0.000000004085965 0.000000000931323
1 F# \1 k, D. B$ L' A* q
0.090525100938976 0.090525101870298 0.090525101404637 0.000000001080430 0.000000000465661: U, P4 z' P\" t8 }% r; k& X' e
0.090525100938976 0.090525101404637 0.090525101171806 -0.000000001502767 0.0000000002328317 `& T+ U7 _. m4 `( f4 g$ G
0.090525101171806 0.090525101404637 0.090525101288222 -0.000000000211169 0.0000000001164153 R. `9 l\" ^% `5 C. M$ Q8 _# Z$ N
0.090525101288222 0.090525101404637 0.090525101346429 0.000000000434631 0.000000000058208
9 ]- d' Z V0 C
0.090525101288222 0.090525101346429 0.090525101317326 0.000000000111731 0.000000000029104
! Q. J: J$ d0 c( M* y
0.090525101288222 0.090525101317326 0.090525101302774 -0.000000000049719 0.000000000014552
( a8 l- \2 e: C' |% ]7 [
0.090525101302774 0.090525101317326 0.090525101310050 0.000000000031006 0.000000000007276
# V5 ?/ N! p) n' u8 I3 s
0.090525101302774 0.090525101310050 0.090525101306412 -0.000000000009357 0.000000000003638
D5 y4 l: h9 o# g, j( _+ f5 s
0.090525101306412 0.090525101310050 0.090525101308231 0.000000000010825 0.000000000001819
, i1 C4 u$ h9 K+ u4 d
0.090525101306412 0.090525101308231 0.090525101307321 0.000000000000734 0.0000000000009090 Q8 r. S7 Q& H! z) s- p5 I
0.090525101306412 0.090525101307321 0.090525101306866 -0.000000000004311 0.000000000000455
5 p) i' M3 \, U8 X; d
0.090525101306866 0.090525101307321 0.090525101307094 -0.000000000001789 0.000000000000227) \7 n1 o+ O\" r9 k
0.090525101307094 0.090525101307321 0.090525101307207 -0.000000000000527 0.000000000000114
% B& A9 Z! O* O0 }. a
0.090525101307207 0.090525101307321 0.090525101307264 0.000000000000103 0.000000000000057
# K\" A: C& F+ i/ k. Y
0.090525101307207 0.090525101307264 0.090525101307236 -0.000000000000212 0.000000000000028
, P) K8 O* o' t! N/ L7 b5 E3 i4 \+ D! D
0.090525101307236 0.090525101307264 0.090525101307250 -0.000000000000054 0.000000000000014
, b* Q: B5 I3 j% K- k( b
0.090525101307250 0.090525101307264 0.090525101307257 0.000000000000025 0.000000000000007
$ m: r7 `0 O7 z4 R$ M. [
0.090525101307250 0.090525101307257 0.090525101307254 -0.000000000000015 0.000000000000004
8 V) k! w7 W& N1 y
0.090525101307254 0.090525101307257 0.090525101307255 0.000000000000005 0.000000000000002
7 N' Z/ q% T2 T$ O$ E
0.090525101307254 0.090525101307255 0.090525101307255 -0.000000000000005 0.000000000000001
; J$ V& C/ O: ]) j0 I/ R
0.090525101307255 0.090525101307255 0.090525101307255 0 0.000000000000000