[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, ^1 g( Y* }0 t$ R0 a
% n=input('请输入迭代次数：');3 k1 K5 L+ P2 m- a+ O6 [4 ?+ J
% qujian=input('请输入初始区间：');* @0 R5 Z7 a7 a
n=100;
2 ~, p! [5 Z4 S; R0 S! @
wucha=0.005;$ j8 V7 Z p' C
qujian=[0 1];
$ s* C( \; U3 L; x+ z) r2 {4 v
a(1)=qujian(1);
. Z0 R7 h) A/ Y% ]2 @4 {- C+ u
b(1)=qujian(2); % y: h/ E+ d7 l0 F! e+ d8 R
a0=a(1);
9 G% ^1 g0 R+ i+ K\" B1 n
b0=b(1);. A$ n% }$ c6 ~% }8 ]
x=qujian;
9 u, m7 ]3 r( i% ?$ X
y=exp(x)+10*x-2;
; [7 T( V& c- o! g' n7 z5 [
y1=y(1); %小于0
K2 H6 _- D8 s! F8 s
y2=y(2); %大于0
7 i1 X* r0 d3 L: ]) @- q4 T
for i=1:n %总迭代次数* a1 s$ @0 Y& b9 C
c(i)=(a+b)/2;\" X1 _, v5 F! c& ~, w' B
f(i)=exp(c(i))+10*(c(i))-2;
7 r; F( _9 i- M! ]! q
kesai_k(i)=(b-a)/2;
5 m& ?/ }* n- ~3 r8 m
if f(i)>09 z0 f8 k3 ^; c\" `
b=c(i);
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b1(i)=c(i);2 x, k2 z' q' ~2 h
a1(i)=a;
& e+ j: e! S& x; W7 z0 ~7 o% {
elseif f(i)<0+ ~$ b4 d2 J- A) I: K
a=c(i);
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a1(i)=c(i);
4 r) r1 z; q9 u9 L
b1(i)=b;
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elseif f(i)==0||kesai_k(i)<=wucha4 }) J% H' P: e6 U) k+ g0 D0 q
disp('精确值解为：');$ y2 |8 B' b( j1 K( V \/ K# L
disp(c(i));# |4 l' e9 O: l3 K% L& W' |
break;! T! F1 y5 Q! ~ k7 V: c2 @. Y
end
% t/ ~4 R\" j1 i+ |- n! i/ a- k# J/ N
end
\" s, s& V$ f0 R7 b6 t0 S
disp('迭代次数：');
( u4 S4 N\" ?' q
fprintf('%d次\n\n',n);
$ G2 i; R0 H5 Y8 V
fprintf('要求误差%f\n\n',wucha);
0 n ?/ _5 t3 R\" r
disp('输出矩阵为：');2 e& f2 j\" E3 b7 w6 G
A=[a0 a1]';
& n3 ]0 P1 M: ]9 }2 s; K6 b
B=[b0 b1]';
5 l, g/ b( P, x7 M' i
format long- U7 ?' m+ W5 D( h2 Q
data_out=[A B c' f' kesai_k']+ r2 M! f# }* `# H% Z
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：; t2 w9 h% i8 Q# O Z
0.0905( \: y5 m- H7 W7 e. I% q. P- L0 ^ X) I) e
0 |% N( o8 o( `8 x
迭代次数： G' ]5 j2 P! L
100次
1 |5 v4 i% R$ [4 w5 r: g
$ q! ~) m1 M2 @& ?
要求误差0.005000
1 y2 h5 e5 c8 c2 G; O. _. W
. O% { f, O+ K2 V
输出矩阵为：( }% t0 T& k6 h {% o# N0 C H: g
* H( z! M9 B$ G( J( k( @* K3 y# Z& Q
data_out =
\" V, h' `5 T* W
1 ]5 u' M i* u2 @, d' @0 g
0 1.000000000000000 0.500000000000000 4.648721270700128 0.500000000000000! U9 x8 w. y1 X1 n7 z* d
0 0.500000000000000 0.250000000000000 1.784025416687741 0.250000000000000
/ w! c H# X1 C; y3 q3 g
0 0.250000000000000 0.125000000000000 0.383148453066826 0.125000000000000
0 A s; f# t1 j
0 0.125000000000000 0.062500000000000 -0.310505541082140 0.062500000000000
% D9 I; X! q4 c& K1 n a. F3 X
0.062500000000000 0.125000000000000 0.093750000000000 0.035785140307826 0.031250000000000
: ~, ^1 y# E, }7 m s
0.062500000000000 0.093750000000000 0.078125000000000 -0.137492192550960 0.015625000000000+ H7 g R. j# z/ A$ O
0.078125000000000 0.093750000000000 0.085937500000000 -0.050886782461907 0.007812500000000
, w& E\" m& ?3 I3 W
0.085937500000000 0.093750000000000 0.089843750000000 -0.007559167670695 0.003906250000000& E. T6 p+ C% K& O& v' S
0.089843750000000 0.093750000000000 0.091796875000000 0.014110895592678 0.001953125000000- [9 ?/ m1 t5 W+ q3 Y! A9 [0 W
0.089843750000000 0.091796875000000 0.090820312500000 0.003275341789827 0.000976562500000
1 K; U# B0 _# H, ^- G2 P0 f! X
0.089843750000000 0.090820312500000 0.090332031250000 -0.002142043419492 0.000488281250000
$ |, ~3 _; F7 B
0.090332031250000 0.090820312500000 0.090576171875000 0.000566616557439 0.000244140625000
7 u1 w) _# o g. H: r
0.090332031250000 0.090576171875000 0.090454101562500 -0.000787721586963 0.0001220703125003 C8 @5 B% `: a8 u) S
0.090454101562500 0.090576171875000 0.090515136718750 -0.000110554553871 0.000061035156250
3 h8 t2 B. @0 ]3 a* l- p0 a% q
0.090515136718750 0.090576171875000 0.090545654296875 0.000228030491991 0.000030517578125
& [/ u3 B. I, B% Z
0.090515136718750 0.090545654296875 0.090530395507813 0.000058737841614 0.000015258789063
) q3 k8 Z\" y' ^% y' D% b% t
0.090515136718750 0.090530395507813 0.090522766113281 -0.000025908387990 0.000007629394531
0 V }2 }, I: m6 @* B; v
0.090522766113281 0.090530395507813 0.090526580810547 0.000016414718847 0.000003814697266
8 p4 Z+ d6 k. p! C( ~+ C( P8 S) Q
0.090522766113281 0.090526580810547 0.090524673461914 -0.000004746836563 0.000001907348633) D8 o( i' L, }) ?, P: A
0.090524673461914 0.090526580810547 0.090525627136230 0.000005833940644 0.000000953674316
# ]' F+ i) Q+ @
0.090524673461914 0.090525627136230 0.090525150299072 0.000000543551916 0.000000476837158$ T; e Q: I F6 f0 c: K
0.090524673461914 0.090525150299072 0.090524911880493 -0.000002101642354 0.0000002384185796 |\" ~\" s! W, m- x
0.090524911880493 0.090525150299072 0.090525031089783 -0.000000779045227 0.000000119209290- f( K9 Z, z4 H8 {7 ~1 a
0.090525031089783 0.090525150299072 0.090525090694427 -0.000000117746657 0.000000059604645
: v# s6 j+ D: J/ f
0.090525090694427 0.090525150299072 0.090525120496750 0.000000212902629 0.000000029802322, H3 s9 r5 m; i! L$ L
0.090525090694427 0.090525120496750 0.090525105595589 0.000000047577986 0.000000014901161! {\" O8 }2 ^3 W3 ]5 @! b
0.090525090694427 0.090525105595589 0.090525098145008 -0.000000035084336 0.000000007450581
0.090525098145008 0.090525105595589 0.090525101870298 0.000000006246825 0.000000003725290
\" ]8 |! ]: d+ t% m: d0 g
0.090525098145008 0.090525101870298 0.090525100007653 -0.000000014418755 0.000000001862645
+ Y- \\" S. Z: E J Y3 s$ h2 e
0.090525100007653 0.090525101870298 0.090525100938976 -0.000000004085965 0.0000000009313237 m6 h6 M* |. r; @! h
0.090525100938976 0.090525101870298 0.090525101404637 0.000000001080430 0.0000000004656612 [% r% c- C0 a8 e z# h
0.090525100938976 0.090525101404637 0.090525101171806 -0.000000001502767 0.0000000002328318 E2 H1 h: B, \( _1 }5 s$ M2 y- n: L
0.090525101171806 0.090525101404637 0.090525101288222 -0.000000000211169 0.000000000116415% [5 Y# Y% b ~6 s3 X9 u
0.090525101288222 0.090525101404637 0.090525101346429 0.000000000434631 0.000000000058208
9 {' x7 S+ ]2 h
0.090525101288222 0.090525101346429 0.090525101317326 0.000000000111731 0.000000000029104
6 S. f- E3 ?. N, V0 s/ C0 N# Z7 l
0.090525101288222 0.090525101317326 0.090525101302774 -0.000000000049719 0.0000000000145525 B9 E* Z\" K# M: k. X% w. f\" o; t6 m
0.090525101302774 0.090525101317326 0.090525101310050 0.000000000031006 0.000000000007276- f) T5 A N( l0 N
0.090525101302774 0.090525101310050 0.090525101306412 -0.000000000009357 0.000000000003638/ r$ @: Y/ L2 b/ m4 U5 p+ {1 @
0.090525101306412 0.090525101310050 0.090525101308231 0.000000000010825 0.000000000001819
j+ H& l) ~- v3 {0 o7 f/ l( L7 G
0.090525101306412 0.090525101308231 0.090525101307321 0.000000000000734 0.000000000000909
0 ^1 T1 y+ P% A4 @% J M# u! n
0.090525101306412 0.090525101307321 0.090525101306866 -0.000000000004311 0.000000000000455
. S. M: Y3 E5 h3 y& b8 {
0.090525101306866 0.090525101307321 0.090525101307094 -0.000000000001789 0.0000000000002272 k# z! S/ K, h3 M, Z# T: N
0.090525101307094 0.090525101307321 0.090525101307207 -0.000000000000527 0.000000000000114
: k4 M\" }+ Y3 n# W0 m0 v\" l
0.090525101307207 0.090525101307321 0.090525101307264 0.000000000000103 0.0000000000000576 Q; P' A' Y. x- F! H+ V& P
0.090525101307207 0.090525101307264 0.090525101307236 -0.000000000000212 0.000000000000028
9 ~9 K\" X Z# u7 Y2 t
0.090525101307236 0.090525101307264 0.090525101307250 -0.000000000000054 0.000000000000014
* ~: P4 e5 ~4 m* L
0.090525101307250 0.090525101307264 0.090525101307257 0.000000000000025 0.000000000000007
% E3 l& A2 T$ V& D3 y) e; N
0.090525101307250 0.090525101307257 0.090525101307254 -0.000000000000015 0.000000000000004
6 u. s5 g! {$ ^) r5 {% U3 R\" F
0.090525101307254 0.090525101307257 0.090525101307255 0.000000000000005 0.000000000000002
) R- W\" p5 q9 A. v( _7 L
0.090525101307254 0.090525101307255 0.090525101307255 -0.000000000000005 0.000000000000001
/ o+ C% t+ M6 P& p- S3 V
0.090525101307255 0.090525101307255 0.090525101307255 0 0.000000000000000