MATLAB程序设计与应用 实验答案 第六章 刘卫国.docx
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MATLAB程序设计与应用 实验答案 第六章 刘卫国.docx
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MATLAB程序设计与应用实验答案第六章刘卫国
1.
(1)
A=randn(10,5)
A=
-0.4326-0.18670.2944-0.3999-1.6041
-1.66560.7258-1.33620.69000.2573
0.1253-0.58830.71430.8156-1.0565
0.28772.18321.62360.71191.4151
-1.1465-0.1364-0.69181.2902-0.8051
1.19090.11390.85800.66860.5287
1.18921.06681.25401.19080.2193
-0.03760.0593-1.5937-1.2025-0.9219
0.3273-0.0956-1.4410-0.0198-2.1707
0.1746-0.83230.5711-0.1567-0.0592
B=mean(A)
B=
0.00130.23100.02530.3588-0.4197
C=std(A)
C=
0.90340.88291.18980.78321.0821
(2)
D=max(max(A))
D=
2.1832
E=min(min(A))
E=
-2.1707
(3)
F=sum(A,2)
F=
-2.3288
-1.3287
0.0105
6.2215
-1.4895
3.3602
4.9201
-3.6964
-3.3998
-0.3025
G=sum(sum(A))
G=
1.9666
(4)
H=sort(A)
H=
-1.6656-0.8323-1.5937-1.2025-2.1707
-1.1465-0.5883-1.4410-0.3999-1.6041
-0.4326-0.1867-1.3362-0.1567-1.0565
-0.0376-0.1364-0.6918-0.0198-0.9219
0.1253-0.09560.29440.6686-0.8051
0.17460.05930.57110.6900-0.0592
0.28770.11390.71430.71190.2193
0.32730.72580.85800.81560.2573
1.18921.06681.25401.19080.5287
1.19092.18321.62361.29021.4151
L=-sort(-A,2,'descend')
L=
-1.6041-0.4326-0.3999-0.18670.2944
-1.6656-1.33620.25730.69000.7258
-1.0565-0.58830.12530.71430.8156
0.28770.71191.41511.62362.1832
-1.1465-0.8051-0.6918-0.13641.2902
0.11390.52870.66860.85801.1909
0.21931.06681.18921.19081.2540
-1.5937-1.2025-0.9219-0.03760.0593
-2.1707-1.4410-0.0956-0.01980.3273
-0.8323-0.1567-0.05920.17460.5711
2.
(1)
x=[0153045607590];
y=[00.25880.50000.70710.86600.96591.0000];
x1=0:
90;
y1=interp1(x,y,x1,'spline')
y1=
Columns1through11
00.01750.03490.05240.06980.08720.10450.12190.13920.15640.1737
Columns12through22
0.19080.20790.22490.24190.25880.27560.29230.30900.32550.34200.3583
Columns23through33
0.37460.39070.40670.42260.43840.45400.46950.48480.50000.51500.5299
Columns34through44
0.54460.55920.57360.58780.60180.61570.62930.64280.65610.66910.6820
Columns45through55
0.69470.70710.71930.73130.74310.75470.76600.77710.78800.79860.8090
Columns56through66
0.81910.82900.83870.84800.85710.86600.87460.88290.89100.89870.9062
Columns67through77
0.91350.92040.92710.93350.93960.94540.95100.95630.96120.96590.9703
Columns78through88
0.97440.97820.98170.98490.98780.99040.99270.99460.99630.99770.9987
Columns89through91
0.99950.99991.0000
x=[01530456075];
y=[00.26790.57741.00001.73203.7320];
x1=0:
75;
y1=interp1(x,y,x1,'spline')
y1=
Columns1through11
00.01840.03650.05450.07240.09020.10790.12550.14310.16070.1784
Columns12through22
0.19610.21380.23170.24970.26790.28630.30480.32360.34270.36200.3817
Columns23through33
0.40170.42210.44290.46410.48580.50790.53050.55370.57740.60170.6266
Columns34through44
0.65200.67800.70460.73170.75930.78760.81630.84560.87540.90580.9367
Columns45through55
0.96811.00001.03251.06581.10031.13641.17431.21451.25721.30281.3516
Columns56through66
1.40411.46041.52111.58631.65651.73201.81311.90021.99362.09372.2008
Columns67through76
2.31522.43742.56752.70602.85323.00953.17523.35063.53613.7320
x=[0153045607590];
y=[00.25880.50000.70710.86600.96591.0000];
y1=polyfit(x,y,5)
y1=
0.00000.0000-0.00000.00000.01740.0000
x=[01530456075];
y=[00.26790.57741.00001.73203.7320];
y1=polyfit(x,y,5)
y1=
0.0000-0.00000.0000-0.00100.02450.0000
(2)
x=[149162536496481100];
y=1:
10;
x1=1:
100;
y1=interp1(x,y,x1,'cubic')
y1=
Columns1through11
1.00001.37291.71252.00002.24052.45512.64942.82923.00003.16363.3186
Columns12through22
3.46613.60693.74223.87294.00004.12374.24354.35994.47304.58324.6907
Columns23through33
4.79584.89885.00005.09935.19665.29215.38575.47775.56815.65705.7446
Columns34through44
5.83095.91606.00006.08296.16476.24546.32496.40356.48106.55776.6334
Columns45through55
6.70826.78236.85566.92817.00007.07127.14167.21137.28047.34877.4164
Columns56through66
7.48357.55007.61597.68127.74597.81027.87397.93728.00008.06238.1242
Columns67through77
8.18558.24648.30688.36688.42638.48548.54418.60248.66038.71788.7749
Columns78through88
8.83178.88818.94429.00009.05559.11079.16559.22019.27449.32849.3821
Columns89through99
9.43549.48849.54129.59359.64569.69739.74869.79969.85029.90059.9505
Column100
10.0000
3.
xi=[165123150123141];
yi=[187126172125148];
P=polyfit(xi,yi,3)
P=
1.0e+003*
-0.00000.0013-0.17798.4330
线性拟合曲线为:
p(x)=1.3x^2—177.9x+8433
4.
(1)
P1=[0,3,2];
P2=[5,-1,2];
P3=[1,0,-0.5];
P=conv(P1,conv(P2,P3))
P=
015.00007.0000-3.50000.5000-2.0000-2.0000
(2)
P1=[0,3,2];
P2=[5,-1,2];
P3=[1,0,-0.5];
P=conv(P1,conv(P2,P3));
Y=roots(P)
Y=
0.7071
0.1000+0.6245i
0.1000-0.6245i
-0.7071
-0.6667
(3)
P1=[0,3,2];
P2=[5,-1,2];
P3=[1,0,-0.5];
P=conv(P1,conv(P2,P3));
k=0:
10;
xi=0.2*k;
Y=polyval(P,xi)
Y=
-2.0000-2.3920-2.6112-1.70242.710415.000042.112094.1408184.9056332.5264560.0000
5.
(1)
[U,fmin]=fminsearch('xiti651',[1,1])
U=
1.0e-004*
-0.06750.1715
fmin=
1.9920e-010
(2)
f=inline('-sin(x)-cos(x.^2)');
fminbnd(f,0,pi)
ans=
0.7310
6.
(1)
x=[pi/6pi/4pi/3pi/2];
f=inline('sin(x).^2+cos(x).^2');
dx=diff(f([x,5*pi/12]))/(pi/12)
dx=
0000
(2)
x=1:
3;
f=inline('sqrt(x.^2+1)');
dx=diff(f([x,4]))
dx=
0.82190.92620.9608
7.
(1)
g=inline('sin(x).^5.*sin(5*x)');
I=quadl(g,0,pi)
I=
0.0982
(2)
g=inline('(1+x.^2)./(1+x.^4)');
I=quad(g,-1,1)
I=
2.2214
(3)
g=inline('(x.*sin(x))./(1+cos(x).^2)');
I=quadl(g,0,pi)
I=
2.4674
(4)
f=inline('abs(cos(x+y))');
dblquad(f,0,pi,0,pi)
ans=
6.2832
9.
(1)
矩阵求逆法:
A=[2,3,5;3,7,4;1,-7,1];
b=[10;3;5];
x=inv(A)*b
x=
-1.8060
-0.5373
3.0448
矩阵除法:
A=[2,3,5;3,7,4;1,-7,1];
b=[10;3;5];
x=A\b
x=
-1.8060
-0.5373
3.0448
矩阵分解法:
A=[2,3,5;3,7,4;1,-7,1];
b=[10;3;5];
[Q,R]=qr(A);
x=R\(Q\b)
x=
-1.8060
-0.5373
3.0448
(2)
矩阵求逆法:
A=[5,1,-1,0;1,0,3,-1;-1,-1,0,5;0,0,2,4];
b=[1;2;3;-1];
x=inv(A)*b
x=
1.4000
-5.9000
0.1000
-0.3000
矩阵除法:
A=[5,1,-1,0;1,0,3,-1;-1,-1,0,5;0,0,2,4];
b=[1;2;3;-1];
x=A\b
x=
1.4000
-5.9000
0.1000
-0.3000
矩阵分解法:
A=[5,1,-1,0;1,0,3,-1;-1,-1,0,5;0,0,2,4];
b=[1;2;3;-1];
[Q,R]=qr(A);
x=R\(Q\b)
x=
1.4000
-5.9000
0.1000
-0.3000
10.
A=[21-11;42-21;21-1-1];
b=[1;2;1];
[x,y]=line_solution(A,b)
原方程组有无穷个解,特解为x,齐次方程组的基础解系为y
Warning:
Rankdeficient,rank=2,tol=4.3512e-015.
>Inline_solutionat11
方程组无解
x=
[]
y=
-0.50000.5000
1.00000
01.0000
00
11.
(1)
f=inline('x-sin(x)./x');
x=fzero(f,0.5)
x=
0.8767
(2)
f=inline('(sin(x).^2).*exp(-0.1.*x)-0.5.*abs(x)');
x=fzero(f,1.5)
x=
1.6738
12.
x=fsolve('xiti612',[0.5,0.5],optimset('Display','off'))
x=
0.5000
y=
0.5000
f=
-0.0509
f=
-0.05090.1173
x=
0.5000
y=
0.5000
f=
-0.0509
f=
-0.05090.1173
x=
0.5000
y=
0.5000
f=
-0.0509
f=
-0.05090.1173
x=
0.6459
y=
0.3739
f=
0.0055
f=
0.00550.0044
x=
0.6459
y=
0.3739
f=
0.0055
f=
0.00550.0044
x=
0.6459
y=
0.3739
f=
0.0055
f=
0.00550.0044
x=
0.6355
y=
0.3734
f=
1.9417e-005
f=
1.0e-004*
0.19420.2589
x=
0.6355
y=
0.3734
f=
1.9425e-005
f=
1.0e-004*
0.19420.2589
x=
0.6355
y=
0.3734
f=
1.9419e-005
f=
1.0e-004*
0.19420.2591
x=
0.6354
y=
0.3734
f=
2.3754e-010
f=
1.0e-009*
0.23750.2957
x=
0.6354
y=
0.3734
f=
7.9432e-009
f=
1.0e-008*
0.79430.5602
x=
0.6354
y=
0.3734
f=
1.8684e-009
f=
1.0e-007*
0.01870.1936
x=
0.63540.3734
13.
x0=0;xf=20;
y1=0;
[x,y]=ode45('xiti6131',[x0,xf],y1)
x=
0
0.5000
1.0000
1.5000
2.0000
2.5000
3.0000
3.5000
4.0000
4.5000
5.0000
5.5000
6.0000
6.5000
7.0000
7.5000
8.0000
8.5000
9.0000
9.5000
10.0000
10.5000
11.0000
11.5000
12.0000
12.5000
13.0000
13.5000
14.0000
14.5000
15.0000
15.5000
16.0000
16.5000
17.0000
17.5000
18.0000
18.5000
19.0000
19.5000
20.0000
y=
0
NaN
NaN
NaN
NaN
NaN
NaN
NaN
NaN
NaN
NaN
NaN
NaN
NaN
NaN
NaN
NaN
NaN
NaN
NaN
NaN
NaN
NaN
NaN
NaN
NaN
NaN
NaN
NaN
NaN
NaN
NaN
NaN
NaN
NaN
NaN
NaN
NaN
NaN
NaN
NaN
(2)
x0=0;xf=20;
[x,y]=ode45('xiti6132',[x0,xf],[-3,2])
[x,y]
此题结果过长,疑似错误或不会做。
14.
f=@(t,x)[-8/3*x
(1)+x
(2)*x(3);-10*x
(2)+10*x(3);-x
(1)*x
(2)+28*x
(2)-x(3)];
t_f=100;
x0=[0;0;1e-10];
[t,x]=ode45(f,[0,t_f],x0)
figure
(2);
plot3(x(:
1),x(:
2),x(:
3));
axis([1040-2020-2020])
t=
0
0.1250
0.2500
0.3750
0.5000
0.5352
0.5705
0.6057
0.6409
0.6761
0.7114
0.7466
0.7818
0.8308
0.8797
0.9286
0.9776
1.0105
1.0434
1.0763
1.1092
1.1421
1.1750
1.2079
1.2409
1.2797
1.3186
1.3575
1.3964
1.4246
1.4528
1.4810
1.5092
1.5374
1.5656
1.5938
1.6220
1.6479
1.6737
1.6996
1.7255
1.7506
1.7757
1.8008
1.8259
1.8507
1.8755
1.9004
1.9252
1.9495
1.9739
1.9982
2.0225
2.0467
2.0709
2.0950
2.1192
2.1432
2.1672
2.1912
2.2152
2.2384
2.2616
2.2848
2.3081
2.3201
2.3321
2.3442
2.3562
2.3682
2.3803
2.3923
2.4044
2.4154
2.4265
2.4376
2.4487
2.4585
2.4684
2.4783
2.4882
2.4976
2.5069
2.5163
2.5257
2.5420
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