PROGRAM:

clc;

clear;

N=4;

x=[1 2 3 4 5];

y=[2 1 5 6 1];

z=2.5;

L=0;

for i=0:N

s=y(i+1);

for j=0:N

if j~=i

s=s*(z-x(j+1))/(x(i+1)-x(j+1));

end

end

L=L+s;

end

L

plot(x,y,z,L,'*r');

%zad11

p=polyfit(x,y,N);

p*24

%zad12

x2=[0 0.1 0.2 0.3 0.4 0.5 0.6]

y2=[2.9 2.8 2.7 2.3 2.1 2.1 1.7]

p2=polyfit(x2,y2,1);

p2

u=p2(1);

w=p2(2);

figure (2);

plot(x2,y2,x2,u*x2+w);

%zad13

x3=[20.5 32.7 51 73.2 95.7]

y3=[765 826 873 942 1032]

p3=polyfit(x3,y3,1)

figure(3);

plot(x3,y3,x3,p3(1)*x3+p3(2));

Wyniki:

%1.1:

x1=[0 0.1 0.2 0.3 0.4 0.5 0.6];

y1=[2.9 2.8 2.7 2.3 2.1 2.1 1.7];

a1=polyfit(x1,y1,1)

Wynik:

a1 = -2.0000 2.9714

%1.2:

x2=[20.5 32.7 51.0 73.2 95.7];

y2=[765 826 873 942 1032];

a2=polyfit(x2,y2,1)

Wynik:

a2 = 3.3949 702.1721

%1.3:

x3=[0 0.2 0.4 0.6 0.8 1.0];

y3=[1.026 0.768 0.648 0.401 0.272 0.193];

a3=polyfit(x3,y3,2)

Wynik:

a3 = 0.3835 -1.2263 1.0239

%1.4:

x4=[0 pi/6 pi/4 pi/3 pi/2];

y4=[0 1/2 sqrt(2)/2 sqrt(3)/2 1];

%a

[a4A,bA]=polyfit(x4,y4,2)

[y4A,delta1]=polyval(a4A,x4,bA)

sumadelta=sum(delta1)

Wynik:

a4A = -0.3346 1.1685 -0.0050

bA = R: [3x3 double] df: 2 normr: 0.0220

y4A = -0.0050 0.5151 0.7064 0.8517 1.0049

delta1 = 0.0217 0.0181 0.0183 0.0181 0.0217

sumadelta = 0.0978

%b

a4B=polyfit(x4,y4,4)

Wynik:

a4B = 0.0288 -0.2043 0.0214 0.9956 -0.0000

%c

k=0:1:16;

x4C=(k*pi)/32;

y4C=polyval(a4A,x4C);

a4C=polyfit(x4C,y4C,2)

Wynik:

a4C = -0.3346 1.1685 -0.0050

%3.1:

a=1;

b=1;

epsilon=0.0001;

x1=(b+a)/2;

n=0;

while (abs(b-a)>epsilon)

n=n+1

x=(a+b)/2

y=(x.^2)-2

ya=(a^2)-2

yb=(b^2)-2

if y~=0

if ya*y<0

b=x

yb=y

else

a=x

ya=y

end

else

break;

end

end

Uniwersytet Warmińsko – Mazurski

W Olsztynie

WYDZIAŁ NAUK TECHNICZNYCH

MECHATRONIKA

Algorytmy i metody numeryczne.

Wykonał:

Mateusz Gołębiewski

Gr III