[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
. H! r9 e' a- Z% Q
% n=input('请输入迭代次数：');
d4 a+ [) L( D; J+ r
% qujian=input('请输入初始区间：');
8 K3 }# g: Z0 P5 H0 A6 v
n=100;& K. |0 Y7 R2 h# w/ t* B
wucha=0.005;
_7 x3 K+ C0 C# E& J; |% i
qujian=[0 1];5 i/ K% F' ^8 s
a(1)=qujian(1);2 _) v6 C& a7 \( g
b(1)=qujian(2);
7 U3 d! r. \2 F7 H n6 a( N! n
a0=a(1);
& K+ X. q7 t Y4 b9 i6 \6 e
b0=b(1);
# V a5 S; w0 K& M$ \, s& Y% @
x=qujian;
0 U3 i\" a* p& ]) e3 w6 M% }: T
y=exp(x)+10*x-2;8 _7 m9 m/ U* T
y1=y(1); %小于05 l7 U: Y* i m' f; S- I
y2=y(2); %大于0
$ ]$ w7 w5 g1 ^+ P6 b4 `
for i=1:n %总迭代次数( _0 L0 }$ T8 d) {5 p\" W Y\" F8 u2 k
c(i)=(a+b)/2;! K) Z$ {/ O1 k- J. J* X
f(i)=exp(c(i))+10*(c(i))-2;& [$ \) @* Q2 l9 p3 {0 O& |
kesai_k(i)=(b-a)/2;
- @' O1 ?9 o4 N* K# x- ~* @
if f(i)>09 S. p, F2 `; w, `3 R
b=c(i);$ p5 Y% U( f$ k/ f$ G& e( W
b1(i)=c(i);, S+ p `* a3 O- U* A
a1(i)=a;' ~0 l# K\" T# r. a' { n7 N\" O
elseif f(i)<0% u8 b5 H( H) ]+ L
a=c(i); y# D, @& {7 H: ^/ ?. C
a1(i)=c(i);
: @ {/ |. J/ o7 u0 C$ V
b1(i)=b;
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elseif f(i)==0||kesai_k(i)<=wucha
disp('精确值解为：');) J5 a8 R0 ?9 Z0 v
disp(c(i));* U/ A\" e6 H3 M/ q8 N# J2 g\" B
break;
, K- h, y; q\" e
end
1 f2 P3 V2 }3 p
end
0 e T\" V% v/ N y% I3 R6 d
disp('迭代次数：');
$ t6 S0 X( B! l7 P& V, N5 V. H0 ^
fprintf('%d次\n\n',n);$ |. ?6 |. k1 _& L
fprintf('要求误差%f\n\n',wucha);
. ]( U/ A% A; z2 T$ o9 c& e
disp('输出矩阵为：');9 o7 y3 R& Q9 N, |- \* ?. D\" j( X
A=[a0 a1]';
, E# x/ ^9 P6 M
B=[b0 b1]';
7 {- [. E: e+ q9 I! _0 i8 D' B: l0 Q
format long
; }- E/ r5 _) A$ G\" k
data_out=[A B c' f' kesai_k']
. f4 Z. H, `. L0 X5 j9 Q
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：
* W\" A2 M# G6 e. K; Y7 f% B
0.0905
% Q/ W4 {5 [+ c& Q' n
$ y: _. l( [9 N/ R. x$ Q% e
迭代次数：
; }4 z7 G2 Q- q0 {& T. n( h
100次
9 O, z! w# P0 [! m% V
1 a7 m8 u% f' Z& ]# m% A
要求误差0.005000
j- o2 {- @( ^8 |, I
: t0 f, Z, x' }& M
输出矩阵为：' I: m* a& b V; A( c
* j* O5 g$ s5 `% y! T
data_out =
4 A6 U; q5 b: [# a+ Q& f: a. b# m
5 I* O0 |% a* U$ @) v9 m1 M
0 1.000000000000000 0.500000000000000 4.648721270700128 0.500000000000000
8 h\" }\" W' l5 o
0 0.500000000000000 0.250000000000000 1.784025416687741 0.250000000000000
\" J6 `4 v5 Q, U1 J: h, D3 W' ]7 s
0 0.250000000000000 0.125000000000000 0.383148453066826 0.125000000000000
+ e7 \+ w* Y- X
0 0.125000000000000 0.062500000000000 -0.310505541082140 0.062500000000000
) [( g. [3 P1 \2 o. e+ ^# C
0.062500000000000 0.125000000000000 0.093750000000000 0.035785140307826 0.031250000000000
; S. p- H0 o. {$ ?& l
0.062500000000000 0.093750000000000 0.078125000000000 -0.137492192550960 0.015625000000000
\" k- J$ B/ {3 c$ T
0.078125000000000 0.093750000000000 0.085937500000000 -0.050886782461907 0.007812500000000
\" g- X( ~' x3 F7 `$ w% b
0.085937500000000 0.093750000000000 0.089843750000000 -0.007559167670695 0.003906250000000
6 o! L6 D: b$ i; A4 @# ^8 y2 c* Q
0.089843750000000 0.093750000000000 0.091796875000000 0.014110895592678 0.001953125000000
+ K: n2 ]' U. F# G- Z
0.089843750000000 0.091796875000000 0.090820312500000 0.003275341789827 0.000976562500000
! {8 m; `0 g: S9 |
0.089843750000000 0.090820312500000 0.090332031250000 -0.002142043419492 0.000488281250000
# M3 m( q3 D- p# ]5 r* b0 o: G7 L
0.090332031250000 0.090820312500000 0.090576171875000 0.000566616557439 0.000244140625000
8 U: `1 Y% s z Y+ N) A. O; i
0.090332031250000 0.090576171875000 0.090454101562500 -0.000787721586963 0.000122070312500 ]0 A) W. M) Y+ T% R0 V
0.090454101562500 0.090576171875000 0.090515136718750 -0.000110554553871 0.000061035156250/ C) }3 x) b4 R! ^4 }( t% S
0.090515136718750 0.090576171875000 0.090545654296875 0.000228030491991 0.0000305175781258 S/ ^6 S$ x- G7 Y
0.090515136718750 0.090545654296875 0.090530395507813 0.000058737841614 0.0000152587890635 s5 M( N9 {5 H+ X
0.090515136718750 0.090530395507813 0.090522766113281 -0.000025908387990 0.000007629394531; Z6 P- h$ a2 {
0.090522766113281 0.090530395507813 0.090526580810547 0.000016414718847 0.000003814697266
$ c) `$ g2 V/ B+ f+ m6 ^
0.090522766113281 0.090526580810547 0.090524673461914 -0.000004746836563 0.000001907348633\" X( A2 D6 b! G
0.090524673461914 0.090526580810547 0.090525627136230 0.000005833940644 0.000000953674316
! I- ?8 k$ H! P. ^4 A
0.090524673461914 0.090525627136230 0.090525150299072 0.000000543551916 0.0000004768371588 ~! |. o6 C\" [9 \# V
0.090524673461914 0.090525150299072 0.090524911880493 -0.000002101642354 0.000000238418579
0 M2 L, @\" K+ M
0.090524911880493 0.090525150299072 0.090525031089783 -0.000000779045227 0.0000001192092905 r$ n0 S% \4 k0 n$ x
0.090525031089783 0.090525150299072 0.090525090694427 -0.000000117746657 0.0000000596046455 t# t\" ^ @0 [ [& N8 E; }2 y! {
0.090525090694427 0.090525150299072 0.090525120496750 0.000000212902629 0.000000029802322\" _1 c9 V. [! r8 A0 H+ ~
0.090525090694427 0.090525120496750 0.090525105595589 0.000000047577986 0.000000014901161* i+ W. i6 n# D# |
0.090525090694427 0.090525105595589 0.090525098145008 -0.000000035084336 0.000000007450581& _1 R3 u) ]! u, L# ~! b7 x) p
0.090525098145008 0.090525105595589 0.090525101870298 0.000000006246825 0.000000003725290
8 A# ^; E9 D! M2 B) `% N
0.090525098145008 0.090525101870298 0.090525100007653 -0.000000014418755 0.000000001862645. V+ u* \. u/ U6 ?4 e\" x
0.090525100007653 0.090525101870298 0.090525100938976 -0.000000004085965 0.000000000931323
- z# }8 ]4 j4 k$ _& v; s2 e
0.090525100938976 0.090525101870298 0.090525101404637 0.000000001080430 0.0000000004656618 m: T+ H9 ?8 e+ E7 l9 a
0.090525100938976 0.090525101404637 0.090525101171806 -0.000000001502767 0.000000000232831
7 P4 K' y1 }& u
0.090525101171806 0.090525101404637 0.090525101288222 -0.000000000211169 0.000000000116415# i- O8 ]* v5 ]\" W7 ^8 l( C
0.090525101288222 0.090525101404637 0.090525101346429 0.000000000434631 0.000000000058208/ ], d\" u5 J$ x
0.090525101288222 0.090525101346429 0.090525101317326 0.000000000111731 0.000000000029104
# x: z: ?! r7 B: {\" ?
0.090525101288222 0.090525101317326 0.090525101302774 -0.000000000049719 0.000000000014552
; l+ ~- X& |\" g+ H
0.090525101302774 0.090525101317326 0.090525101310050 0.000000000031006 0.000000000007276% C0 y t* o8 ~: g5 Q E/ j
0.090525101302774 0.090525101310050 0.090525101306412 -0.000000000009357 0.000000000003638+ p& S- h5 F( f\" k! L7 U. S' ^
0.090525101306412 0.090525101310050 0.090525101308231 0.000000000010825 0.0000000000018190 O' Z* b3 I. C2 A) w9 G
0.090525101306412 0.090525101308231 0.090525101307321 0.000000000000734 0.000000000000909' s) S/ Y' H4 ?, ^8 n% a
0.090525101306412 0.090525101307321 0.090525101306866 -0.000000000004311 0.000000000000455
& Y8 M# l, P- `
0.090525101306866 0.090525101307321 0.090525101307094 -0.000000000001789 0.000000000000227
' p, F3 e7 b# J3 S$ q4 O X' }
0.090525101307094 0.090525101307321 0.090525101307207 -0.000000000000527 0.000000000000114
: Q\" h# X/ T) k. v3 m- N' H
0.090525101307207 0.090525101307321 0.090525101307264 0.000000000000103 0.0000000000000576 ^, n- Z' f\" V( Y
0.090525101307207 0.090525101307264 0.090525101307236 -0.000000000000212 0.000000000000028
, I y% ]. K; o& }+ }
0.090525101307236 0.090525101307264 0.090525101307250 -0.000000000000054 0.0000000000000145 d) B- B- U' C: I$ }' O
0.090525101307250 0.090525101307264 0.090525101307257 0.000000000000025 0.000000000000007
* w. K2 o' g: t
0.090525101307250 0.090525101307257 0.090525101307254 -0.000000000000015 0.000000000000004
; F n6 |5 t: l' J1 y
0.090525101307254 0.090525101307257 0.090525101307255 0.000000000000005 0.000000000000002% h* _1 n! z4 ]
0.090525101307254 0.090525101307255 0.090525101307255 -0.000000000000005 0.0000000000000010 E7 ~' r6 U' g/ J) v; B
0.090525101307255 0.090525101307255 0.090525101307255 0 0.000000000000000