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//Example 11.9
//QR Method
//Page no. 360
clc;close;clear;
A=[2,-1,0;-1,2,-1;0,-1,2];
deff('y=c(i,j)','y=A(j,j)/sqrt((A(i,j)^2+A(j,j)^2))')
deff('y=s2(i,j)','y=A(i,j)/sqrt((A(i,j)^2+A(j,j)^2))')
disp(A,'A=')
l0=0;f=1;m=0;s=0;w=0;
for n=1:5
for j=1:2
for k=1:2
V(j,k)=A(j,k)
end
end
disp(V,'V=')
p=poly(V,'x');
disp('=0',p);
a=roots(p);
for j=1:2
printf('\na(%i) = %f',j,a(j))
end
if(abs(a(1)-V(1,1))<=abs(a(2)-V(1,1)))
a=a(1)
else
a=a(2)
end
printf('\na = %f\n',a)
s=s+a;
A=A-a*eye()
R=A;Q=eye(3,3);
for j=1:2
for i=j+1:3
for k=1:3 //C matrix evaluation
for l=1:3
if(k==l)
if(k==i | k==j)
C(k,l)=c(i,j)
else
C(k,l)=1
end
end
if(k>l)
if(k==i & l==j)
C(k,l)=-1*s2(i,j)
else
C(k,l)=0
end
end
if(k<l)
if(k==j & l==i)
C(k,l)=s2(i,j)
else
C(k,l)=0
end
end
end
end
R=C*R;
Q=Q*C';
end
end
disp(Q,'Q=',R,'R=')
disp(Q*R,'Q*R=')
A=R*Q;
disp(A,'A=')
end
l1=l0+s;
for i=2:3
for j=2:3
V(i-1,j-1)=A(i,j)
end
end
disp(V,'V=')
p=poly(V,'x');
disp('=0',p);
a=roots(p);
for j=1:2
printf('\na(%i) = %f',j,a(j))
end
l2=l1+a(1)
l3=l1+a(2)
disp(l3,'l3=',l2,'l2=',l1,'l1=')
printf('\n\n\nNote : Values of V varies in each step resulting in different results due to error in book calculation')
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