[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
7 B+ S4 e3 J f$ Y% \
% n=input('请输入迭代次数：'); U' _* G$ \. P) L) y$ t
% qujian=input('请输入初始区间：');
7 K3 d1 u\" d7 H* }! O$ |
n=100;. J$ c9 ] s' h% Y+ M, u D
wucha=0.005;1 K `0 ~* @7 ]) E\" D
qujian=[0 1];
8 U& f [$ H# a
a(1)=qujian(1);* K\" F0 a- o5 H# ?
b(1)=qujian(2); 4 H( v/ Y$ Z: z; D
a0=a(1);4 R: a; c. K! |, G; p
b0=b(1);/ ^; O\" C8 o0 R\" J% |, V
x=qujian;- W# Y, i2 [& F/ k3 `+ W
y=exp(x)+10*x-2;) |( K# P+ b3 n# c
y1=y(1); %小于0
+ d+ q! K: B; F: C
y2=y(2); %大于0! H. l% q/ \; \( O
for i=1:n %总迭代次数* z6 ~; y5 c% d2 f, M
c(i)=(a+b)/2;
; g: h# q! E% K+ ?, |& J8 a
f(i)=exp(c(i))+10*(c(i))-2;8 w5 ]1 e& z4 I0 ?+ ?* ~
kesai_k(i)=(b-a)/2;- a# H2 ]& V; R% s. a1 @, ]
if f(i)>05 P0 [9 m$ x# W9 E\" Y
b=c(i);
/ _: z) e$ R, h. c
b1(i)=c(i);
1 i1 n\" n8 S! u6 F# H
a1(i)=a;+ w$ f5 [+ t! @, j+ ^. h4 C
elseif f(i)<0 F+ l& f# X- R$ d7 y( F( U% j
a=c(i);
1 t, [5 F) A/ J$ |7 Y
a1(i)=c(i);. b; l\" y: Y& }! j8 Q
b1(i)=b;6 O, J* D0 E' h. b\" K+ X$ A- R
elseif f(i)==0||kesai_k(i)<=wucha. D9 I; \* R, x: v- x
disp('精确值解为：');
' O e* n& E# h\" W% k# L5 l
disp(c(i));1 l3 ^. {; P$ s+ `, p
break;
! [* T8 Q\" \' y. v) K( u7 h
end9 ~3 x) s8 J4 X* J1 h3 e* C' x
end
|- j) u\" @& X I! @- f
disp('迭代次数：');
# o, I- Q7 \\" u
fprintf('%d次\n\n',n);
. Z7 T) w% a; p+ x\" s
fprintf('要求误差%f\n\n',wucha);
) P, n' [: Z# g
disp('输出矩阵为：');
\" `: {3 h1 Z+ Q' c M5 y- p
A=[a0 a1]';/ o6 ~; I6 r( F
B=[b0 b1]';+ X) y: A( ?4 C7 l% J. ?& A0 K( r( k) N
format long
* F8 y3 Q. |5 u7 W2 ^
data_out=[A B c' f' kesai_k']
+ ]( C/ @1 w( S* p2 b$ _2 N$ p9 Y
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：
- c/ o5 } ]/ M) |5 `$ M
0.0905 Y+ N+ T. U. l+ h+ j# c* D) t) s
* R- `* z, J\" K8 Q6 C% V\" F
迭代次数：# l8 K$ ^; N/ d0 }3 U: D
100次6 k\" p$ |# W, [/ j* d
7 S0 Q6 `/ u+ o; [' I/ g m9 i
要求误差0.005000
\" Y/ Z9 }* R% y$ N
% V8 ^: L4 J\" `- }- }) z. c% d3 x
输出矩阵为：
. @5 c m6 Y Q
4 {# l( \1 S5 ~
data_out =
( C3 w; c2 E% P, K\" U
, S; {3 L# F, ^- j9 q/ Y\" H
0 1.000000000000000 0.500000000000000 4.648721270700128 0.500000000000000
( I% H) m$ f( ^
0 0.500000000000000 0.250000000000000 1.784025416687741 0.250000000000000
9 I$ Y) }, @% }$ u- \; Z! V
0 0.250000000000000 0.125000000000000 0.383148453066826 0.125000000000000, g6 `# r5 j0 p3 w
0 0.125000000000000 0.062500000000000 -0.310505541082140 0.062500000000000
8 w+ ^7 F: l& [6 a6 h
0.062500000000000 0.125000000000000 0.093750000000000 0.035785140307826 0.031250000000000
( ~# R* L4 L) w8 a, u\" g
0.062500000000000 0.093750000000000 0.078125000000000 -0.137492192550960 0.015625000000000
- V; |' O0 q7 O( p2 n! o' U% v
0.078125000000000 0.093750000000000 0.085937500000000 -0.050886782461907 0.007812500000000
9 |- T( t* @2 c1 A7 Y
0.085937500000000 0.093750000000000 0.089843750000000 -0.007559167670695 0.003906250000000
, S; X0 L' x1 c
0.089843750000000 0.093750000000000 0.091796875000000 0.014110895592678 0.001953125000000
6 \1 A$ P& O) j7 y0 I
0.089843750000000 0.091796875000000 0.090820312500000 0.003275341789827 0.000976562500000& p9 n' o! ?9 o: F
0.089843750000000 0.090820312500000 0.090332031250000 -0.002142043419492 0.000488281250000
0 s! a( n# { `$ y' x5 V4 m
0.090332031250000 0.090820312500000 0.090576171875000 0.000566616557439 0.0002441406250001 e- i$ _3 g8 I\" \
0.090332031250000 0.090576171875000 0.090454101562500 -0.000787721586963 0.000122070312500
+ F% t* x1 G5 P3 o% c
0.090454101562500 0.090576171875000 0.090515136718750 -0.000110554553871 0.000061035156250- I$ r9 d9 r6 v3 y
0.090515136718750 0.090576171875000 0.090545654296875 0.000228030491991 0.000030517578125
\" E# C* x- i( O! Z: P+ D- U
0.090515136718750 0.090545654296875 0.090530395507813 0.000058737841614 0.000015258789063; z* t+ C% V5 E3 F
0.090515136718750 0.090530395507813 0.090522766113281 -0.000025908387990 0.000007629394531
! T4 q& B3 ~# P2 P# U' W
0.090522766113281 0.090530395507813 0.090526580810547 0.000016414718847 0.000003814697266
) b& h) z8 n: L3 B\" Q! R5 Q
0.090522766113281 0.090526580810547 0.090524673461914 -0.000004746836563 0.000001907348633
, T. i8 |8 I3 @9 f$ w
0.090524673461914 0.090526580810547 0.090525627136230 0.000005833940644 0.000000953674316& I6 }& \ ]2 P1 p( }7 l5 i& ?- E
0.090524673461914 0.090525627136230 0.090525150299072 0.000000543551916 0.0000004768371582 n1 e* _! v- G
0.090524673461914 0.090525150299072 0.090524911880493 -0.000002101642354 0.000000238418579
, [4 V/ z; R. r
0.090524911880493 0.090525150299072 0.090525031089783 -0.000000779045227 0.000000119209290' n5 L/ C: @3 S3 J; j\" W; G& j% c
0.090525031089783 0.090525150299072 0.090525090694427 -0.000000117746657 0.000000059604645- K; J e5 I4 U7 }; U
0.090525090694427 0.090525150299072 0.090525120496750 0.000000212902629 0.000000029802322
% v% a9 Q1 ~. I% E
0.090525090694427 0.090525120496750 0.090525105595589 0.000000047577986 0.000000014901161( V3 M; }. w' C& [- U! |) \
0.090525090694427 0.090525105595589 0.090525098145008 -0.000000035084336 0.0000000074505819 s7 ~/ n0 h) V4 ?) ^8 P( U8 N1 l
0.090525098145008 0.090525105595589 0.090525101870298 0.000000006246825 0.000000003725290; w+ S: D\" \8 o! n! X8 q7 ?+ @) m
0.090525098145008 0.090525101870298 0.090525100007653 -0.000000014418755 0.000000001862645
) A. W0 p. ]) r\" }$ h
0.090525100007653 0.090525101870298 0.090525100938976 -0.000000004085965 0.000000000931323 P6 K G( g, L
0.090525100938976 0.090525101870298 0.090525101404637 0.000000001080430 0.000000000465661/ M0 l5 g5 `\" O- u7 ~6 D: ?& l
0.090525100938976 0.090525101404637 0.090525101171806 -0.000000001502767 0.000000000232831
; h( V# k! Y. l) ?! X
0.090525101171806 0.090525101404637 0.090525101288222 -0.000000000211169 0.000000000116415
/ n: H$ G& U' L- r w% r
0.090525101288222 0.090525101404637 0.090525101346429 0.000000000434631 0.000000000058208
& C% c0 ]& q2 r2 F% C# |7 t
0.090525101288222 0.090525101346429 0.090525101317326 0.000000000111731 0.000000000029104
2 ^8 ~% O) ]/ Q
0.090525101288222 0.090525101317326 0.090525101302774 -0.000000000049719 0.000000000014552
) m/ z4 g; i: \7 H0 O8 g2 |- `, ^
0.090525101302774 0.090525101317326 0.090525101310050 0.000000000031006 0.000000000007276+ A. d. O8 F0 [5 y; S) s! I
0.090525101302774 0.090525101310050 0.090525101306412 -0.000000000009357 0.000000000003638' L7 r$ w. i5 ?9 }& y$ z\" l& |& A
0.090525101306412 0.090525101310050 0.090525101308231 0.000000000010825 0.000000000001819
% y2 K2 X, g3 p
0.090525101306412 0.090525101308231 0.090525101307321 0.000000000000734 0.000000000000909
2 l: p# d/ w! d2 S0 ^4 f
0.090525101306412 0.090525101307321 0.090525101306866 -0.000000000004311 0.0000000000004552 o; v- N! U; D% `) g
0.090525101306866 0.090525101307321 0.090525101307094 -0.000000000001789 0.000000000000227- K ~2 w) g! F' a1 g
0.090525101307094 0.090525101307321 0.090525101307207 -0.000000000000527 0.000000000000114+ ]! a6 j! R& F3 T4 y8 [' i
0.090525101307207 0.090525101307321 0.090525101307264 0.000000000000103 0.0000000000000578 t0 r4 B/ ~- G! g
0.090525101307207 0.090525101307264 0.090525101307236 -0.000000000000212 0.000000000000028% N) L7 I. ~. _( W, X: ?
0.090525101307236 0.090525101307264 0.090525101307250 -0.000000000000054 0.000000000000014) ~# ~\" Y- L5 I$ V8 G
0.090525101307250 0.090525101307264 0.090525101307257 0.000000000000025 0.000000000000007
0 u; u; x: h% M3 n* W; u$ M
0.090525101307250 0.090525101307257 0.090525101307254 -0.000000000000015 0.0000000000000043 A1 @- l- ~3 j: J
0.090525101307254 0.090525101307257 0.090525101307255 0.000000000000005 0.000000000000002
, `2 P0 M/ y6 P: C; y9 V
0.090525101307254 0.090525101307255 0.090525101307255 -0.000000000000005 0.000000000000001
2 ?5 V8 N; A n' n7 F3 @+ ]4 D
0.090525101307255 0.090525101307255 0.090525101307255 0 0.000000000000000