[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\" o1 L\" a# f/ G$ x6 T! Y
% n=input('请输入迭代次数：');
) I8 i1 p/ |5 q6 s
% qujian=input('请输入初始区间：');
/ P) v/ G3 H) M. d }3 K; _: [
n=100;$ _! j! J/ G0 u
wucha=0.005;- B7 V/ {! I* k/ T; |
qujian=[0 1];
) h/ m, ?$ h* ]1 O/ V
a(1)=qujian(1);8 t, Z) \! S4 `4 f\" O- O- A. ^
b(1)=qujian(2); % k: i% m* N\" s! M
a0=a(1);4 l7 \7 z1 o$ v$ l
b0=b(1);
( c$ Q% f! b+ V( z; X0 ^$ D\" ~3 Q- }
x=qujian;
7 e& L- `; x. |5 J
y=exp(x)+10*x-2;) j6 S x, R3 b6 E
y1=y(1); %小于0' U+ Y0 J% E; a) o- h6 b
y2=y(2); %大于0
+ u4 s! {% p& x; {: M1 W
for i=1:n %总迭代次数3 b6 b) Q6 ]9 A5 d8 |/ W9 e% F. T( w8 o+ I
c(i)=(a+b)/2;; P' [) F' y( q+ j, ], H
f(i)=exp(c(i))+10*(c(i))-2;
6 Y) @\" J\" C9 ?% X4 e1 D\" z( l3 F' d
kesai_k(i)=(b-a)/2;
( v; b/ A4 r, O
if f(i)>07 X) f: n5 J& U
b=c(i);
, t ~\" }! L+ w8 C+ F# K( `0 l1 H
b1(i)=c(i);
U4 X9 i, T* S+ T! k
a1(i)=a;6 |' V7 ]* I+ r. ^
elseif f(i)<0
* E: C' p( ~% R
a=c(i);
* z! b' f4 N* f/ u4 i1 T
a1(i)=c(i);
, g' l' b8 }# r& T0 `2 x# X
b1(i)=b;) F( F6 q8 H' Q8 q( s0 s: |5 f. d
elseif f(i)==0||kesai_k(i)<=wucha* a\" I7 p2 m0 t- Z4 T\" m7 M
disp('精确值解为：');5 F) b& L1 S5 V# u' C5 f9 H
disp(c(i));
{1 F2 p5 t) ~( w* o3 v. w8 ~/ x
break;% O' c: z1 b4 S2 M# m4 P- i
end/ C, ~: w f! A% V5 X3 R, h3 A
end
/ v+ v' j6 [9 t# G$ }% j X
disp('迭代次数：');/ j5 O5 \8 \# t# t4 \& d# I
fprintf('%d次\n\n',n);, y! @: M& y6 F$ g1 a3 X6 j& ^
fprintf('要求误差%f\n\n',wucha);
7 M- `! Y0 w9 w9 K7 V
disp('输出矩阵为：');6 h0 b$ Q+ y- H; Z6 W- n& C) I3 c% @
A=[a0 a1]';
K& u) ?. Z' x, m, ^
B=[b0 b1]';
6 D\" l* X' ^- R
format long0 ~4 Q, l: w8 n( h, R; m
data_out=[A B c' f' kesai_k']
% e! J5 j3 Z; e. M& x ]% z( h7 a
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：
6 Y3 b0 H. t1 |4 f3 L
0.0905
) r+ f* }+ U& k' _
; Y* p# x: F& g
迭代次数：8 N1 D2 y, P( z* `
100次
9 v( L6 Z0 ]5 x4 s2 q
1 N( A% j4 ^- P3 ?: s6 L* K
要求误差0.005000
0 q$ I1 R6 m7 @* v0 d
$ D- |% ^ v. t
输出矩阵为：4 g0 p V4 ^) ]% u/ v, m4 a2 k. e
+ Q/ W0 g0 z+ e# f
data_out =
8 e3 u$ v\" Z' K e0 w
* W# z- R$ M' K6 {1 O
0 1.000000000000000 0.500000000000000 4.648721270700128 0.500000000000000& |4 X( \7 \2 Z. r- A$ \4 n
0 0.500000000000000 0.250000000000000 1.784025416687741 0.2500000000000003 `# V* H2 m$ k3 [9 E2 A\" E
0 0.250000000000000 0.125000000000000 0.383148453066826 0.1250000000000008 n( I8 Q( ~0 c, m8 \. h
0 0.125000000000000 0.062500000000000 -0.310505541082140 0.0625000000000003 z; H3 Y8 [1 P6 `. k
0.062500000000000 0.125000000000000 0.093750000000000 0.035785140307826 0.031250000000000: S5 k8 Y2 R/ N7 m& m
0.062500000000000 0.093750000000000 0.078125000000000 -0.137492192550960 0.0156250000000009 z! G- G% G, K$ x- s. l5 Q
0.078125000000000 0.093750000000000 0.085937500000000 -0.050886782461907 0.007812500000000
. e( u( A, d# z8 v
0.085937500000000 0.093750000000000 0.089843750000000 -0.007559167670695 0.003906250000000( ?. A T$ c/ H$ ]4 n E/ }: i
0.089843750000000 0.093750000000000 0.091796875000000 0.014110895592678 0.001953125000000( ]' Q: p1 z, Q; L5 a7 e4 p
0.089843750000000 0.091796875000000 0.090820312500000 0.003275341789827 0.000976562500000
\" X3 D) b Y3 z4 `* ~
0.089843750000000 0.090820312500000 0.090332031250000 -0.002142043419492 0.000488281250000
0 F7 D! o! t. f7 @
0.090332031250000 0.090820312500000 0.090576171875000 0.000566616557439 0.000244140625000
( v\" X5 \\" A1 ?7 n* G\" R) S0 j/ q
0.090332031250000 0.090576171875000 0.090454101562500 -0.000787721586963 0.000122070312500
# @) k) H5 e2 C$ e4 `5 E; g+ }$ n9 n
0.090454101562500 0.090576171875000 0.090515136718750 -0.000110554553871 0.0000610351562505 Z# U% d$ O8 P: F$ c' z
0.090515136718750 0.090576171875000 0.090545654296875 0.000228030491991 0.000030517578125
0 v) i' g& v1 ]
0.090515136718750 0.090545654296875 0.090530395507813 0.000058737841614 0.000015258789063
# [1 E$ W9 ~5 A\" A0 a) e: T
0.090515136718750 0.090530395507813 0.090522766113281 -0.000025908387990 0.000007629394531 j5 {. t9 M D0 S
0.090522766113281 0.090530395507813 0.090526580810547 0.000016414718847 0.000003814697266- w8 s; I& {9 j* c7 _. u
0.090522766113281 0.090526580810547 0.090524673461914 -0.000004746836563 0.000001907348633
2 w) R- D\" I/ A, ^
0.090524673461914 0.090526580810547 0.090525627136230 0.000005833940644 0.000000953674316+ C5 X\" w$ Q+ Z\" D. r
0.090524673461914 0.090525627136230 0.090525150299072 0.000000543551916 0.000000476837158
) g* ]$ H5 J- M* }& E1 I
0.090524673461914 0.090525150299072 0.090524911880493 -0.000002101642354 0.000000238418579) M0 ~. S; J: A
0.090524911880493 0.090525150299072 0.090525031089783 -0.000000779045227 0.000000119209290* O$ m- u4 F. ^+ b7 q- z7 I- ]
0.090525031089783 0.090525150299072 0.090525090694427 -0.000000117746657 0.000000059604645
& a, @* @5 d$ u; P\" A% C) s; _+ ?9 r
0.090525090694427 0.090525150299072 0.090525120496750 0.000000212902629 0.0000000298023229 T* ?5 i: r- }% i/ I
0.090525090694427 0.090525120496750 0.090525105595589 0.000000047577986 0.000000014901161
$ }+ M/ V4 p3 v& q9 G( I$ x
0.090525090694427 0.090525105595589 0.090525098145008 -0.000000035084336 0.000000007450581
4 C- h5 a! ]! [# }
0.090525098145008 0.090525105595589 0.090525101870298 0.000000006246825 0.000000003725290+ Z. T0 \- ^* \: O* q# v
0.090525098145008 0.090525101870298 0.090525100007653 -0.000000014418755 0.000000001862645
# G) m9 p5 R2 n& ]* U+ V& j
0.090525100007653 0.090525101870298 0.090525100938976 -0.000000004085965 0.000000000931323! T% O9 J( |7 L& Z g6 _
0.090525100938976 0.090525101870298 0.090525101404637 0.000000001080430 0.000000000465661/ `5 x h6 ~7 K F- u8 k7 ~
0.090525100938976 0.090525101404637 0.090525101171806 -0.000000001502767 0.0000000002328317 s. q. i& E) D
0.090525101171806 0.090525101404637 0.090525101288222 -0.000000000211169 0.000000000116415$ U\" x; [2 e! K
0.090525101288222 0.090525101404637 0.090525101346429 0.000000000434631 0.000000000058208
3 R4 M: M7 j m2 y- n7 g8 |$ |4 @/ ?
0.090525101288222 0.090525101346429 0.090525101317326 0.000000000111731 0.000000000029104
) x) R$ s* `+ [4 e: B
0.090525101288222 0.090525101317326 0.090525101302774 -0.000000000049719 0.000000000014552- k( l/ e8 T, }7 ]0 k' F; R
0.090525101302774 0.090525101317326 0.090525101310050 0.000000000031006 0.000000000007276
v% w, W) A: N4 J\" ?5 _
0.090525101302774 0.090525101310050 0.090525101306412 -0.000000000009357 0.000000000003638! C4 |6 u$ l. H
0.090525101306412 0.090525101310050 0.090525101308231 0.000000000010825 0.000000000001819( r2 ?- S+ A+ X% n1 v* Q% R) E! i; @
0.090525101306412 0.090525101308231 0.090525101307321 0.000000000000734 0.000000000000909\" U, f. w\" s0 j% s) ~& g
0.090525101306412 0.090525101307321 0.090525101306866 -0.000000000004311 0.0000000000004556 U/ P# k$ K\" Y. h( }4 C' J6 A
0.090525101306866 0.090525101307321 0.090525101307094 -0.000000000001789 0.000000000000227
; t9 p# t) F( P/ f+ F4 M' G. l X
0.090525101307094 0.090525101307321 0.090525101307207 -0.000000000000527 0.000000000000114\" j0 K4 S7 v* o, n0 l
0.090525101307207 0.090525101307321 0.090525101307264 0.000000000000103 0.000000000000057( P2 _: @. ^/ w5 L( u( W
0.090525101307207 0.090525101307264 0.090525101307236 -0.000000000000212 0.000000000000028 s, ]8 Y# ]9 h4 ~9 N9 ^' K\" i
0.090525101307236 0.090525101307264 0.090525101307250 -0.000000000000054 0.000000000000014
3 ?/ t4 c! j6 u: O
0.090525101307250 0.090525101307264 0.090525101307257 0.000000000000025 0.000000000000007* F, Z/ C. e& C C% C7 L
0.090525101307250 0.090525101307257 0.090525101307254 -0.000000000000015 0.000000000000004
\" |9 T\" N* o D& d: B
0.090525101307254 0.090525101307257 0.090525101307255 0.000000000000005 0.000000000000002
% Y. i8 a4 [# ^0 U8 W5 _2 `
0.090525101307254 0.090525101307255 0.090525101307255 -0.000000000000005 0.0000000000000011 {9 {# @* ]: E
0.090525101307255 0.090525101307255 0.090525101307255 0 0.000000000000000