[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
3 ` t9 @8 F. b- i1 s# h
% n=input('请输入迭代次数：');& m/ y+ V' [2 B9 _' k/ W
% qujian=input('请输入初始区间：');
6 }+ u& W3 |$ W: k/ H+ F/ L/ b9 }1 R$ W
n=100;
' c2 t5 q, U\" y$ s4 y
wucha=0.005;
j1 a j' k* i: P4 H) k
qujian=[0 1];
8 @$ \& `; d3 l7 O( `
a(1)=qujian(1);2 E5 y8 F0 _; `) }+ j
b(1)=qujian(2); ) G9 ?+ \9 a\" E2 _$ S. p- }
a0=a(1);
5 m* a9 A\" w- x- f1 b0 v
b0=b(1);
\" M1 L\" H; a/ R6 c
x=qujian;6 V, L7 N! y9 p Q
y=exp(x)+10*x-2;7 |1 S0 d. ]& y\" ?0 U7 U: T' s
y1=y(1); %小于0
3 H$ k& ]* I8 `, I b
y2=y(2); %大于0
; f' y( ]% G% Q\" w! I' A6 K
for i=1:n %总迭代次数
2 C4 F% L0 }* Q
c(i)=(a+b)/2;! V' g- r\" F w% M3 g4 d; x
f(i)=exp(c(i))+10*(c(i))-2;
! G% ]+ f' ?7 Z' P- G
kesai_k(i)=(b-a)/2;0 [4 h7 Q9 W9 O) F3 T\" A6 z u
if f(i)>0\" ? x3 C% C4 I7 Q2 _' f
b=c(i);7 T# Y6 N1 O, Q9 I
b1(i)=c(i);' W0 ?. g% e5 b! { C) X
a1(i)=a;
2 [2 z: c' g5 _9 X4 y3 z, U
elseif f(i)<0
. E1 x9 | n, x: L3 @. \
a=c(i);& j7 ?6 W5 U. s% C
a1(i)=c(i);
* q/ N+ E# }; f( C& ~
b1(i)=b;! ~- w6 A2 q9 B
elseif f(i)==0||kesai_k(i)<=wucha; f8 z1 `6 `# n! V
disp('精确值解为：');2 ~/ w) b6 ^* v- L' E1 Z% T% A
disp(c(i));
9 J: j( q2 n2 z1 t
break;
. n5 B' C. p: {2 l; [! k. P( \
end
& n. N+ D6 W* p! b1 \- F) r1 U* n) _
end
- F\" p3 o( n! L4 C6 N( G* ?
disp('迭代次数：');
fprintf('%d次\n\n',n);
9 c7 F& D. z5 G# e: S' i) U
fprintf('要求误差%f\n\n',wucha); r; u; c8 h p Y& l E
disp('输出矩阵为：');
. T% ^, ?! ]; G3 k
A=[a0 a1]';, A+ e/ F$ y( K/ S
B=[b0 b1]';
Y7 s3 N) `* W6 ?9 R, U: `
format long, f- U) ^8 S6 l* \ Q0 s5 T, D+ m
data_out=[A B c' f' kesai_k']& ^2 j8 Y5 o; |/ P
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 I9 T1 J: S3 }
0.09059 N: `\" G4 \' M* a) D
+ E& n. J1 ?/ y( l\" k
迭代次数：2 s4 V1 U# y8 o6 r0 n9 w
100次
& z! w* P1 @\" ^; W9 G8 b3 ?
# M4 R* Q4 g# V$ F8 v\" r7 v( Y
要求误差0.005000$ a. n+ {3 s' B3 t0 D4 Y* T5 v
7 b: T( ^$ j/ Z5 A
输出矩阵为：
2 t% E# {% c. E- A- u
9 Q\" U8 G3 ~% I4 X2 a$ `\" N- o+ h
data_out =
' b. }6 Z N( J& ?
1 c, W# k+ T7 f0 U/ w
0 1.000000000000000 0.500000000000000 4.648721270700128 0.5000000000000005 \7 }\" o' J- A4 `0 Q
0 0.500000000000000 0.250000000000000 1.784025416687741 0.2500000000000004 B) A' [9 t9 Z, Z4 A\" l
0 0.250000000000000 0.125000000000000 0.383148453066826 0.125000000000000
7 w) ^9 s* l+ b) T
0 0.125000000000000 0.062500000000000 -0.310505541082140 0.0625000000000006 q( S! a4 F' R; Q
0.062500000000000 0.125000000000000 0.093750000000000 0.035785140307826 0.031250000000000# F f! n/ u4 j
0.062500000000000 0.093750000000000 0.078125000000000 -0.137492192550960 0.015625000000000
& o+ |4 O3 ~& R( L$ J8 S
0.078125000000000 0.093750000000000 0.085937500000000 -0.050886782461907 0.007812500000000
: E9 Y* t- E\" o7 R
0.085937500000000 0.093750000000000 0.089843750000000 -0.007559167670695 0.003906250000000/ j\" m! [2 Q- t, n
0.089843750000000 0.093750000000000 0.091796875000000 0.014110895592678 0.001953125000000
: ]2 O* m6 d. ]
0.089843750000000 0.091796875000000 0.090820312500000 0.003275341789827 0.000976562500000
4 a+ A+ L [7 _# h6 H* i7 _
0.089843750000000 0.090820312500000 0.090332031250000 -0.002142043419492 0.000488281250000
7 l0 {, _' i: c$ M/ t5 i) }6 d
0.090332031250000 0.090820312500000 0.090576171875000 0.000566616557439 0.0002441406250004 `( G# z% o( B4 B. ?! l! A
0.090332031250000 0.090576171875000 0.090454101562500 -0.000787721586963 0.0001220703125006 N f2 k9 ^1 j3 X% s
0.090454101562500 0.090576171875000 0.090515136718750 -0.000110554553871 0.000061035156250
0 W7 w. V1 R. J8 g8 G
0.090515136718750 0.090576171875000 0.090545654296875 0.000228030491991 0.0000305175781254 U2 `, Z8 ?$ E/ d
0.090515136718750 0.090545654296875 0.090530395507813 0.000058737841614 0.0000152587890635 u+ V* _. O' F3 | Q9 Q& a2 n
0.090515136718750 0.090530395507813 0.090522766113281 -0.000025908387990 0.000007629394531
1 }' { S, h$ [6 F9 C/ v
0.090522766113281 0.090530395507813 0.090526580810547 0.000016414718847 0.000003814697266% g M' M2 r5 S& j: S _, g6 ~\" V
0.090522766113281 0.090526580810547 0.090524673461914 -0.000004746836563 0.000001907348633
2 V' ~0 W' [7 r9 E* t
0.090524673461914 0.090526580810547 0.090525627136230 0.000005833940644 0.000000953674316
I' v' y7 w/ A. P\" Z7 X
0.090524673461914 0.090525627136230 0.090525150299072 0.000000543551916 0.000000476837158
$ c! s! r( P! O. ?1 Y
0.090524673461914 0.090525150299072 0.090524911880493 -0.000002101642354 0.000000238418579+ A# t; S) y9 V
0.090524911880493 0.090525150299072 0.090525031089783 -0.000000779045227 0.000000119209290& k+ _6 i: K& q* l+ H
0.090525031089783 0.090525150299072 0.090525090694427 -0.000000117746657 0.000000059604645
4 X( |\" ?4 ?/ D, ~& c
0.090525090694427 0.090525150299072 0.090525120496750 0.000000212902629 0.000000029802322( }6 Y( l* f; n( y! L
0.090525090694427 0.090525120496750 0.090525105595589 0.000000047577986 0.000000014901161
! x) B2 E7 x7 K9 c8 |/ e# I
0.090525090694427 0.090525105595589 0.090525098145008 -0.000000035084336 0.000000007450581
5 P2 q* \9 @, J! `$ l& j1 w0 Y8 Q
0.090525098145008 0.090525105595589 0.090525101870298 0.000000006246825 0.000000003725290: X) ?3 v: |0 A
0.090525098145008 0.090525101870298 0.090525100007653 -0.000000014418755 0.000000001862645
7 ^9 c8 ^0 }6 d: t! I/ m* J
0.090525100007653 0.090525101870298 0.090525100938976 -0.000000004085965 0.0000000009313231 f# L1 z7 X- P7 D. V
0.090525100938976 0.090525101870298 0.090525101404637 0.000000001080430 0.000000000465661, C! {! h0 O* X: F- _, Q5 X+ f
0.090525100938976 0.090525101404637 0.090525101171806 -0.000000001502767 0.000000000232831
4 h- F' S* u9 a$ J6 J; k/ F
0.090525101171806 0.090525101404637 0.090525101288222 -0.000000000211169 0.000000000116415
8 p5 t. S) { m6 p, V/ r% B2 C7 v. `
0.090525101288222 0.090525101404637 0.090525101346429 0.000000000434631 0.000000000058208
+ w3 G- V+ E, J/ m( b\" d H
0.090525101288222 0.090525101346429 0.090525101317326 0.000000000111731 0.0000000000291048 p k* I$ w% j. w, C
0.090525101288222 0.090525101317326 0.090525101302774 -0.000000000049719 0.000000000014552
* {4 W1 z3 v- ?
0.090525101302774 0.090525101317326 0.090525101310050 0.000000000031006 0.000000000007276$ e$ J; f0 V# p) @
0.090525101302774 0.090525101310050 0.090525101306412 -0.000000000009357 0.000000000003638
* U- w; v* K0 W; ^! s. x/ |\" }
0.090525101306412 0.090525101310050 0.090525101308231 0.000000000010825 0.0000000000018194 ~2 Z( e2 x/ |& Q5 g( R
0.090525101306412 0.090525101308231 0.090525101307321 0.000000000000734 0.000000000000909# h# F( p% d6 T# D# N7 E& S
0.090525101306412 0.090525101307321 0.090525101306866 -0.000000000004311 0.000000000000455
! y\" z3 E; \1 E8 S+ Q
0.090525101306866 0.090525101307321 0.090525101307094 -0.000000000001789 0.000000000000227\" g; m; X- \& x' z4 w: \; k
0.090525101307094 0.090525101307321 0.090525101307207 -0.000000000000527 0.000000000000114$ q2 Y) P$ B0 B: P0 Y3 X+ }. P% S
0.090525101307207 0.090525101307321 0.090525101307264 0.000000000000103 0.000000000000057* r! ?. G/ a, b( C' c
0.090525101307207 0.090525101307264 0.090525101307236 -0.000000000000212 0.000000000000028
% [* T$ y, p! u0 [) v8 `! S
0.090525101307236 0.090525101307264 0.090525101307250 -0.000000000000054 0.000000000000014: ~; b7 \4 g6 {( s/ R/ r* o6 p5 H- K
0.090525101307250 0.090525101307264 0.090525101307257 0.000000000000025 0.000000000000007
x) I! R/ L+ \8 t
0.090525101307250 0.090525101307257 0.090525101307254 -0.000000000000015 0.000000000000004
- d. `9 C( S: ]# S
0.090525101307254 0.090525101307257 0.090525101307255 0.000000000000005 0.000000000000002# z4 |# B: }\" S5 Z( ]5 G; K+ `
0.090525101307254 0.090525101307255 0.090525101307255 -0.000000000000005 0.000000000000001& n, W- g1 H% {' U% h4 W
0.090525101307255 0.090525101307255 0.090525101307255 0 0.000000000000000