KKKA05 Tenta 2011-03-10 Carmen Arevalo

Contents

format short g

Uppgift 1

A=[ 13  39   2  57 28
    -4 -12   0 -19 -9
     3   0  -9   2  1
     6  17   9   5  7
    19  42 -17 107 44];
B=[  -53  57 -145
      18 -18   49
      -7 -11  -27
       0  18   -4
    -103  69 -286];
[L,U,P]=lu(A)

L =
            1            0            0            0            0
      0.68421            1            0            0            0
      0.31579       0.3641            1            0            0
      0.15789     -0.64615      0.26499            1            0
     -0.21053     -0.30769     0.065431   -0.0018642            1
U =
           19           42          -17          107           44
            0       10.263       13.632      -16.211      -2.1053
            0            0       9.4051      -22.887      -6.1282
            0            0            0      -19.304      -5.6838
            0            0            0            0    0.0057621
P =
     0     0     0     0     1
     1     0     0     0     0
     0     0     0     1     0
     0     0     1     0     0
     0     1     0     0     0

Solve Ly=PB

Y=L\(P*B);

Solve Ux=y

X=U\Y

X =
            1           -1            1
           -1            1           -2
            1            1            3
           -1            1           -2
            1           -1            1

Check solution: norm of residual should be very small

norm(A*X-B)

ans =
  3.2517e-014

Uppgift 2

f=@(x)x.^3.*sin(x)-x.^2-10*x+7;
xp=linspace(-8,8);
yp=f(xp);
figure(1)
plot(xp,yp)
grid

There are 4 roots near -6, -4, 0 and 6.

[x1,r1]=fzero(f,-6)
[x2,r2]=fzero(f,-4)
[x3,r3]=fzero(f,0)
[x4,r4]=fzero(f,6)

x1 =
       -6.151
r1 =
  4.2633e-014
x2 =
      -3.7546
r2 =
     0
x3 =
      0.67369
r3 =
     0
x4 =
       6.6441
r4 =
 -2.1316e-014

Uppgift 3

T=0:20:180;
r=[-1.31 0 1.32 2.60 3.95 5.29 6.59 7.90 9.24 10.55];

The independent variable must be r, because we want a function T(r)

figure(2)
plot(r,T,'o')
xlabel('r')
ylabel('T')

Fitting a straight line, y=p(1)x+p(2)

p=polyfit(r,T,1)
disp('The fitted line is y = p(1) x + p(2)')
rp=linspace(r(1),r(end));
Tp=polyval(p,rp);
figure(3)
plot(r,T,'o',rp,Tp)
xlabel('r')
ylabel('T')
legend('data','fit','Location','best')

p =
       15.163       20.052
The fitted line is y = p(1) x + p(2)

Published with MATLAB® 7.10