1 %Zad2a
2 w1 = [-5,5];
3 w2 = [-3,1];
4 w3 = [1,2];
5 X = zeros(3,3);
6 X(1,1) = ((w1(1) - 0) * (w1(1) - w2(1)) * (w1(1) - w3(1)));
7 X(2,2) = ((w2(1) - 0) * (w2(1) - w1(1)) * (w2(1) - w3(1)));
8 X(3,3) = ((w3(1) - 0) * (w3(1) - w1(1)) * (w3(1) - w2(1)));
9 Y = zeros(3,1);
10 Y(1,1) = w1(2);
11 Y(2,1) = w2(2);
12 Y(3,1) = w3(2);
13 display(X);
14 display(Y);
15 A = inv(X) * Y;
16 display(A);
17 fprintf(' W(x)=%f*x^3 + %f*x^2 + %f*x\n', A(3,1), A(2,1), A(1,1));
18 x=[-5:1:5];
19 y=zeros(1,11);
20 for i=1:11
21 y(i)=A(1,1)+A(2,1)*x(i)+A(3,1)*x(i)^2;
22 end
23 plot(x, y);
24 grid on;
25 hold on;
26 vector_x=[w1(1,1), w2(1,1), w3(1,1)];
27 vector_y=zeros(1, 3);
28 for i=1:3
29 vector_y(1,1)=vector_y(1,1)+A(i,1)*w1(1,1)^(i-1);
30 vector_y(1,2)=vector_y(1,2)+A(i,1)*w2(1,1)^(i-1);
31 vector_y(1,3)=vector_y(1,3)+A(i,1)*w3(1,1)^(i-1);
32 end
33 plot(vector_x,vector_y,'rx');
34 plot(w1(1,1),w1(1,2),'--gs');
35 plot(w2(1,1),w2(1,2),'--gs');
36 plot(w3(1,1),w3(1,2),'--gs');
37 title('Interpolacja Lagrange’a - zadanie 2a');
38 ylabel('Os y');
39 xlabel('Os x');