[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- X5 |( L- p8 X/ Z, {9 N
% n=input('请输入迭代次数：');
* `' M4 `$ [/ V
% qujian=input('请输入初始区间：');, v' e9 N7 } F. i [
n=100;
: s$ f$ n\" ]8 z( d. [9 k+ B
wucha=0.005;
& m' g* p1 |3 B\" ?5 g) I
qujian=[0 1];7 q. r5 P) ?3 s9 d; }
a(1)=qujian(1);& c. U0 m6 G% H0 l9 _, o' x
b(1)=qujian(2);
- U% l- J' s) j B& @4 \
a0=a(1);
* ^ V\" J2 `( g% }) k
b0=b(1);
# F7 f# c& M1 R# o x
x=qujian;
\" A, J2 N$ c8 ?4 D* [: J& A/ V
y=exp(x)+10*x-2;
/ P3 _5 b3 x+ b8 U
y1=y(1); %小于0& ~: R# t6 V- k: T- n
y2=y(2); %大于0% C) s: I% W' w# ^3 E0 \# t\" R
for i=1:n %总迭代次数
. Z% B+ `: k1 I0 M
c(i)=(a+b)/2;) t9 @6 `* x4 A5 I3 C) T) W) c
f(i)=exp(c(i))+10*(c(i))-2;
. ?2 G9 q1 X8 S V8 F
kesai_k(i)=(b-a)/2;
4 H5 o9 q$ y; l' }
if f(i)>0* R4 ?1 N- }\" X2 J3 t
b=c(i); x3 h- \2 x# m2 ?, r\" M7 [
b1(i)=c(i);
6 [2 s1 c' m2 `3 L9 P, B
a1(i)=a; r Y( Y! |& X/ v
elseif f(i)<0! D$ o- w$ |, C
a=c(i);& m7 s! K& V0 F. ~! P0 w% z; ]
a1(i)=c(i);
7 Q0 U6 v3 n$ ]
b1(i)=b; _5 Y, H: O4 a, `
elseif f(i)==0||kesai_k(i)<=wucha
* F2 p8 u; w( e, y( U$ F
disp('精确值解为：');* v. U. r: e6 E1 i! N6 y6 r
disp(c(i));
; K( ^3 g& {& ^5 S$ f' m
break;& P: \$ y/ M' ~! r4 j$ _( O
end
+ [) k# ~ y& a' O
end
2 M1 X; f* @0 J/ T! E
disp('迭代次数：');
7 E* ]/ r- n3 V: X$ |, X* G
fprintf('%d次\n\n',n);! o! C* K) Y* F% B$ W& W0 L, y# W' ?- {
fprintf('要求误差%f\n\n',wucha);# V9 l+ v2 m4 h% P- D( g
disp('输出矩阵为：');# j* G7 w2 S$ Z! X4 I
A=[a0 a1]';1 _, M7 x9 J) N
B=[b0 b1]';7 x1 B. _1 q' m' {# Z
format long4 ~0 L1 m' K \
data_out=[A B c' f' kesai_k']
+ [3 }1 x\" T1 k' F
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：: | u' d# {$ c\" ^\" i0 m
0.0905
4 n' O$ h' \2 d
% H8 h. B; G\" z) b+ ?! V% Y
迭代次数：' K$ T4 d! ^0 X
100次 h. c9 {0 {0 a5 [$ C Z
( {' y3 {1 f' f, w1 u
要求误差0.0050007 B- p0 g% \\" ?& K z6 B
4 g8 h Y3 Y8 t6 X
输出矩阵为：
+ [2 C# b) Q# i
( i2 ]; n; Y1 F1 g n J* Z4 @
data_out =5 Z: d\" Z- z9 [: V8 z0 e' K* I, N
|- W: _- T8 U
0 1.000000000000000 0.500000000000000 4.648721270700128 0.5000000000000002 k# A. ^+ s7 N- `) K$ w
0 0.500000000000000 0.250000000000000 1.784025416687741 0.250000000000000
; v% v. ?# u7 j+ w+ t
0 0.250000000000000 0.125000000000000 0.383148453066826 0.125000000000000, w! _. L# B- |6 d
0 0.125000000000000 0.062500000000000 -0.310505541082140 0.062500000000000& Q6 z3 c7 E5 |5 [\" t
0.062500000000000 0.125000000000000 0.093750000000000 0.035785140307826 0.031250000000000
2 \ B; j! l0 E& q
0.062500000000000 0.093750000000000 0.078125000000000 -0.137492192550960 0.015625000000000) [; H; G3 H4 d
0.078125000000000 0.093750000000000 0.085937500000000 -0.050886782461907 0.007812500000000
% i' ?/ d2 k9 v- H! i4 [& E
0.085937500000000 0.093750000000000 0.089843750000000 -0.007559167670695 0.003906250000000. }) q4 L4 f4 g1 o8 s; i
0.089843750000000 0.093750000000000 0.091796875000000 0.014110895592678 0.001953125000000
$ a' b% U1 F; O! d2 A4 ^
0.089843750000000 0.091796875000000 0.090820312500000 0.003275341789827 0.000976562500000
3 w; m1 v, z9 _2 x ~# o
0.089843750000000 0.090820312500000 0.090332031250000 -0.002142043419492 0.000488281250000
M$ |1 z# |; ^! u, w
0.090332031250000 0.090820312500000 0.090576171875000 0.000566616557439 0.0002441406250001 [+ N4 D5 {2 F
0.090332031250000 0.090576171875000 0.090454101562500 -0.000787721586963 0.000122070312500& u# x- q8 \3 Q\" s/ D
0.090454101562500 0.090576171875000 0.090515136718750 -0.000110554553871 0.000061035156250! U+ W1 @9 O# X% O, @5 b
0.090515136718750 0.090576171875000 0.090545654296875 0.000228030491991 0.000030517578125
9 p! I. l\" y8 Y' S- r: V& u' R
0.090515136718750 0.090545654296875 0.090530395507813 0.000058737841614 0.000015258789063
. A( t: d2 ^4 y- h! p$ g& m5 j
0.090515136718750 0.090530395507813 0.090522766113281 -0.000025908387990 0.000007629394531: r7 x9 p( P7 Z6 i: O$ H! p
0.090522766113281 0.090530395507813 0.090526580810547 0.000016414718847 0.000003814697266! p5 T S4 N3 [. K8 ~- b
0.090522766113281 0.090526580810547 0.090524673461914 -0.000004746836563 0.000001907348633
9 J8 _ H0 q0 \\" m; r3 }! Q- n
0.090524673461914 0.090526580810547 0.090525627136230 0.000005833940644 0.0000009536743165 t3 q8 m: D' ?8 j8 s# m5 Z8 r
0.090524673461914 0.090525627136230 0.090525150299072 0.000000543551916 0.000000476837158
1 u4 q4 K9 g3 N5 {( v: _
0.090524673461914 0.090525150299072 0.090524911880493 -0.000002101642354 0.0000002384185795 u& d6 W- h f- w( Q
0.090524911880493 0.090525150299072 0.090525031089783 -0.000000779045227 0.000000119209290* ~4 V1 I7 h( o2 Q
0.090525031089783 0.090525150299072 0.090525090694427 -0.000000117746657 0.000000059604645
: A; l) Y4 k n. h$ J0 b
0.090525090694427 0.090525150299072 0.090525120496750 0.000000212902629 0.000000029802322
- r% T9 S' { }0 ]) z# P
0.090525090694427 0.090525120496750 0.090525105595589 0.000000047577986 0.000000014901161. e; ?' {: a* O' ]! ]
0.090525090694427 0.090525105595589 0.090525098145008 -0.000000035084336 0.0000000074505816 @9 L+ G5 V2 x6 l8 r) G\" Q
0.090525098145008 0.090525105595589 0.090525101870298 0.000000006246825 0.000000003725290
2 ~ |: w4 h\" B3 F4 U- B9 j' m5 n
0.090525098145008 0.090525101870298 0.090525100007653 -0.000000014418755 0.000000001862645, M! Z4 ~8 T7 ?3 i- i: Y
0.090525100007653 0.090525101870298 0.090525100938976 -0.000000004085965 0.000000000931323
; C& _, U- e9 k S, J
0.090525100938976 0.090525101870298 0.090525101404637 0.000000001080430 0.000000000465661
+ z D0 w4 j; s6 v- k
0.090525100938976 0.090525101404637 0.090525101171806 -0.000000001502767 0.0000000002328317 h. F! o; ]' G: L5 ^
0.090525101171806 0.090525101404637 0.090525101288222 -0.000000000211169 0.000000000116415
! W N6 }7 I6 D4 c. e
0.090525101288222 0.090525101404637 0.090525101346429 0.000000000434631 0.000000000058208
, S# Y$ y1 L! A' w7 L2 k) O
0.090525101288222 0.090525101346429 0.090525101317326 0.000000000111731 0.000000000029104
6 N' Q c! G7 `9 V! g+ g
0.090525101288222 0.090525101317326 0.090525101302774 -0.000000000049719 0.000000000014552
1 L9 _! v* B v2 c6 t
0.090525101302774 0.090525101317326 0.090525101310050 0.000000000031006 0.000000000007276
6 w1 w, n4 [2 A( ]! C! `
0.090525101302774 0.090525101310050 0.090525101306412 -0.000000000009357 0.0000000000036389 G' @! \; [/ u' K8 o9 C
0.090525101306412 0.090525101310050 0.090525101308231 0.000000000010825 0.000000000001819+ }\" l\" Y$ O\" D: F
0.090525101306412 0.090525101308231 0.090525101307321 0.000000000000734 0.000000000000909* f7 j( V: y\" k+ x) E+ [
0.090525101306412 0.090525101307321 0.090525101306866 -0.000000000004311 0.000000000000455
% ?/ e9 t* N/ P, X# J\" a2 b
0.090525101306866 0.090525101307321 0.090525101307094 -0.000000000001789 0.000000000000227
' W- G# A8 ]6 f! _- e
0.090525101307094 0.090525101307321 0.090525101307207 -0.000000000000527 0.0000000000001140 z% ~+ T, h\" y* e
0.090525101307207 0.090525101307321 0.090525101307264 0.000000000000103 0.000000000000057\" }: H( W& R0 m2 U0 m0 K% l9 M
0.090525101307207 0.090525101307264 0.090525101307236 -0.000000000000212 0.0000000000000283 ^6 V. D, u) [# C- c$ a4 O
0.090525101307236 0.090525101307264 0.090525101307250 -0.000000000000054 0.000000000000014
8 V6 V% h* O+ t, K& P1 R) B
0.090525101307250 0.090525101307264 0.090525101307257 0.000000000000025 0.000000000000007+ g/ b% o) F' a
0.090525101307250 0.090525101307257 0.090525101307254 -0.000000000000015 0.000000000000004
3 C9 s: ?. p2 P( L5 j7 M
0.090525101307254 0.090525101307257 0.090525101307255 0.000000000000005 0.000000000000002$ E\" ?$ ]* y4 X$ ?! e
0.090525101307254 0.090525101307255 0.090525101307255 -0.000000000000005 0.000000000000001
& n' U5 J3 T# X/ A. s
0.090525101307255 0.090525101307255 0.090525101307255 0 0.000000000000000