[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 |正序浏览

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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
9 ~8 H: j; @7 v% g: _. {\" h1 \1 N
% n=input('请输入迭代次数：');0 `8 [& Z- {, ]; i- f0 M
% qujian=input('请输入初始区间：');3 L, n+ J* |& K
n=100;' b6 {/ G- q1 o6 z2 f! b- a
wucha=0.005;
& J& ^4 v* F* p
qujian=[0 1];' l2 G& F! g& d2 U+ P3 E( M5 ?
a(1)=qujian(1);\" Y& L4 \9 R& | a2 G1 {
b(1)=qujian(2); 2 o) L$ x. I1 }, Y! J5 G- r/ b7 k3 ?
a0=a(1);9 |( A6 u! V8 U& ]- l
b0=b(1);9 P! \# x+ m9 Z. `, z
x=qujian;
8 q. Z+ \+ P) `& t
y=exp(x)+10*x-2;
5 A0 \ l7 H& v8 d) j9 Y) Q3 o; H
y1=y(1); %小于0
0 C6 S4 u! T$ N. A
y2=y(2); %大于0
: b% N. _6 @6 O
for i=1:n %总迭代次数/ P, ]7 h/ ~! X* p5 w0 T& T6 o0 K
c(i)=(a+b)/2;+ I3 C( F* ^& z
f(i)=exp(c(i))+10*(c(i))-2;0 h+ f* R: B\" P, h! y, t1 v: L& w
kesai_k(i)=(b-a)/2;( M1 e8 }+ Y) x; C& R
if f(i)>0$ z9 V) l5 X6 x r' W# U
b=c(i);\" h3 t3 \) ~7 q9 U1 W } ]* `! t9 H) d+ _# n
b1(i)=c(i);/ r3 q( W- M$ c) g. J6 X3 I
a1(i)=a;
6 \& Q\" o: l& C; o2 q
elseif f(i)<0
2 j. W% Y: L/ N5 n0 m
a=c(i);% W+ L/ p# u9 O\" q- C! J, E9 O
a1(i)=c(i);
1 H# r/ K: q; F9 t
b1(i)=b;/ G# e8 y& p+ F, c
elseif f(i)==0||kesai_k(i)<=wucha
2 m\" q9 P7 ^; d6 I! T
disp('精确值解为：');
5 l. [4 `0 p% P8 E4 w\" Y* B
disp(c(i));2 l2 L+ y4 J# W7 N1 M
break;
( R; ^5 d* a% O/ b; E+ R0 H$ V
end
% J5 z8 }' Q$ l( n. w3 \
end1 H3 I+ b$ x4 K: e, R\" M
disp('迭代次数：');
* C2 D\" q: W8 F) U$ A
fprintf('%d次\n\n',n);
) q& q; t* M0 p
fprintf('要求误差%f\n\n',wucha);
7 L! x* W' K+ q' z4 B
disp('输出矩阵为：');* v! G( l6 a9 L
A=[a0 a1]';
- M\" d5 F& C i# X
B=[b0 b1]';
7 ^! g3 K\" P4 \& T; w8 c1 W$ s
format long
! `) ~1 s% I- Y9 a8 l
data_out=[A B c' f' kesai_k']! F- \5 N1 Q! m4 I* i3 V. 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：/ }! V7 k+ g) O, M\" J. y
0.0905% E, J/ w7 h8 S v
0 P4 k5 S3 Y0 n; i e4 D& K
迭代次数：, K% a\" i& w5 S1 q9 b\" ?
100次
% @2 _( |5 ~$ \2 e+ z L: j
7 i7 {) L6 f/ [& r
要求误差0.0050007 w# C! y9 d( D7 I, n\" b6 @# }
1 d# v7 w% r& s/ }; P# F, A% l0 C
输出矩阵为：
' F\" J: _ I, ^\" S5 V+ o4 ^
) i+ m2 \* D' k5 d6 ^, t; C
data_out =- g2 o+ ?0 l3 V. i h( l\" w2 u
: ^! \+ V9 m$ f/ V\" J, `
0 1.000000000000000 0.500000000000000 4.648721270700128 0.5000000000000003 n; D- [3 G$ k3 A% W! I* [8 t5 z
0 0.500000000000000 0.250000000000000 1.784025416687741 0.250000000000000( V# t' _) x. j& P5 I
0 0.250000000000000 0.125000000000000 0.383148453066826 0.125000000000000
% p7 F8 U/ n\" F\" Y7 v3 b. \- l* Q
0 0.125000000000000 0.062500000000000 -0.310505541082140 0.062500000000000
- I2 M( R# _8 V/ h) N4 c* h
0.062500000000000 0.125000000000000 0.093750000000000 0.035785140307826 0.031250000000000 ?' F k/ n, z; o$ h7 Y
0.062500000000000 0.093750000000000 0.078125000000000 -0.137492192550960 0.015625000000000\" W6 n2 t6 D' _8 X- R; O
0.078125000000000 0.093750000000000 0.085937500000000 -0.050886782461907 0.007812500000000
- o% c/ z6 y* Q# }( r2 q
0.085937500000000 0.093750000000000 0.089843750000000 -0.007559167670695 0.003906250000000# ]4 r! ?% D' C7 K
0.089843750000000 0.093750000000000 0.091796875000000 0.014110895592678 0.001953125000000
8 i% W; l( G/ {) f [4 r/ Z' b
0.089843750000000 0.091796875000000 0.090820312500000 0.003275341789827 0.000976562500000
; w' G1 G. n5 E/ f% Q7 ^
0.089843750000000 0.090820312500000 0.090332031250000 -0.002142043419492 0.000488281250000
5 F' W# Y i7 U! O& ?- M\" W: i
0.090332031250000 0.090820312500000 0.090576171875000 0.000566616557439 0.000244140625000\" p. f& a/ b# j* B5 ]
0.090332031250000 0.090576171875000 0.090454101562500 -0.000787721586963 0.000122070312500
+ ~7 d2 V3 b4 s) I8 M/ ^+ c
0.090454101562500 0.090576171875000 0.090515136718750 -0.000110554553871 0.000061035156250
0 L& M+ a+ r2 U$ _8 L4 {
0.090515136718750 0.090576171875000 0.090545654296875 0.000228030491991 0.0000305175781258 a. `& O5 h* Q/ n1 H; ]2 o9 }
0.090515136718750 0.090545654296875 0.090530395507813 0.000058737841614 0.000015258789063* }. t* G( E# L& w6 g+ G+ u- M# }
0.090515136718750 0.090530395507813 0.090522766113281 -0.000025908387990 0.000007629394531
) V0 R; C8 K# _, o( l$ j' {+ K
0.090522766113281 0.090530395507813 0.090526580810547 0.000016414718847 0.000003814697266
\" T7 N4 R8 S1 M; v* @
0.090522766113281 0.090526580810547 0.090524673461914 -0.000004746836563 0.000001907348633$ h- W& b# L0 Q+ D; @8 p
0.090524673461914 0.090526580810547 0.090525627136230 0.000005833940644 0.000000953674316
) W6 H+ G: h- d) G2 Q
0.090524673461914 0.090525627136230 0.090525150299072 0.000000543551916 0.000000476837158
/ p8 l* K+ [6 ?- C9 K9 i) S
0.090524673461914 0.090525150299072 0.090524911880493 -0.000002101642354 0.000000238418579
: D+ x3 ~# i7 _, S
0.090524911880493 0.090525150299072 0.090525031089783 -0.000000779045227 0.000000119209290
# C# N7 Q- [9 {$ J% @
0.090525031089783 0.090525150299072 0.090525090694427 -0.000000117746657 0.000000059604645
. E- K2 x! ]* V* n/ ^) b; m+ Q. ^& t
0.090525090694427 0.090525150299072 0.090525120496750 0.000000212902629 0.000000029802322
+ [6 I7 D9 p' C2 I5 L6 W
0.090525090694427 0.090525120496750 0.090525105595589 0.000000047577986 0.000000014901161: L1 a2 [/ q) f! p2 w
0.090525090694427 0.090525105595589 0.090525098145008 -0.000000035084336 0.000000007450581
% A: N. v( _' ]' S% C
0.090525098145008 0.090525105595589 0.090525101870298 0.000000006246825 0.000000003725290/ @7 c9 ~- ]- A! _2 Q
0.090525098145008 0.090525101870298 0.090525100007653 -0.000000014418755 0.000000001862645
7 v4 A. n9 m& A' ~* I
0.090525100007653 0.090525101870298 0.090525100938976 -0.000000004085965 0.000000000931323
; Y; o3 E6 T- W+ k
0.090525100938976 0.090525101870298 0.090525101404637 0.000000001080430 0.0000000004656619 E6 d& P8 M2 K5 P: x
0.090525100938976 0.090525101404637 0.090525101171806 -0.000000001502767 0.000000000232831\" r, f7 Q\" v- T2 N# a2 [) i
0.090525101171806 0.090525101404637 0.090525101288222 -0.000000000211169 0.0000000001164157 W) y0 r% G6 L; I8 X
0.090525101288222 0.090525101404637 0.090525101346429 0.000000000434631 0.000000000058208
5 K\" n( W$ t. F' s7 g
0.090525101288222 0.090525101346429 0.090525101317326 0.000000000111731 0.000000000029104
% {' K, F0 ^ q- @, G7 {$ N( v
0.090525101288222 0.090525101317326 0.090525101302774 -0.000000000049719 0.000000000014552
1 m% d3 W2 F% V\" M! h
0.090525101302774 0.090525101317326 0.090525101310050 0.000000000031006 0.0000000000072764 X2 C' [% M. J\" O# J
0.090525101302774 0.090525101310050 0.090525101306412 -0.000000000009357 0.000000000003638) `# K9 v3 U$ T& l+ e. a% G4 o2 p
0.090525101306412 0.090525101310050 0.090525101308231 0.000000000010825 0.000000000001819
( K8 ]' K( i9 ^0 `9 Z6 h
0.090525101306412 0.090525101308231 0.090525101307321 0.000000000000734 0.000000000000909. j1 K ^# |# F8 V
0.090525101306412 0.090525101307321 0.090525101306866 -0.000000000004311 0.000000000000455: ]- ~2 w) u' g& M1 |) [
0.090525101306866 0.090525101307321 0.090525101307094 -0.000000000001789 0.000000000000227
1 _% |\" w) ~. B+ E [, s
0.090525101307094 0.090525101307321 0.090525101307207 -0.000000000000527 0.000000000000114
. V% Y$ t, ?0 L6 d7 f1 Y
0.090525101307207 0.090525101307321 0.090525101307264 0.000000000000103 0.0000000000000579 X\" S1 ^8 q1 Z- ~4 M/ j- W
0.090525101307207 0.090525101307264 0.090525101307236 -0.000000000000212 0.000000000000028% T! b. I6 J9 Q4 ^2 \4 T$ _
0.090525101307236 0.090525101307264 0.090525101307250 -0.000000000000054 0.000000000000014
8 f; t7 i. ]9 h+ z# q
0.090525101307250 0.090525101307264 0.090525101307257 0.000000000000025 0.000000000000007+ ~0 Q P- J1 \, G0 D( y
0.090525101307250 0.090525101307257 0.090525101307254 -0.000000000000015 0.000000000000004
$ B; n* }& q2 A z6 N+ r\" _. x
0.090525101307254 0.090525101307257 0.090525101307255 0.000000000000005 0.0000000000000023 F1 a- `* I& g8 K8 S2 `& k
0.090525101307254 0.090525101307255 0.090525101307255 -0.000000000000005 0.000000000000001, b/ w0 o6 c* w3 J
0.090525101307255 0.090525101307255 0.090525101307255 0 0.000000000000000