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//Example 11.7
//Jacobi's Method
//Page no. 355
clc;close;clear;
A=[1,1,1/2;1,1,1/4;1/2,1/4,2];
C=A;
V=[sqrt(2),0,1/2;sqrt(2),0,1/4;3/(4*sqrt(2)),-1/(4*sqrt(2)),2]
S=eye(3,3)
disp(A,"A =")
VI=0;
for i=1:3
for j=1:3
if(i~=j)
VI=VI+A(i,j)^2 //initial off diag norm
end
end
end
VI=sqrt(VI);
VF=VI*10^-7; //final threshold
V1=VI/3;
o=poly(0,"o");
for i=1:3
for q=2:3
for p=q-1:-1:1
if(A(p,q)>V1)
a=-A(p,q);
b=(A(p,p)-A(q,q))/2
if(b~=0)
w=b*abs(1/b)*(a/sqrt(a^2+b^2));
else
w=(a/sqrt(a^2+b^2));
end
sin0=w/sqrt(2*(1+sqrt(1-w^2)));
cos0=sqrt(1-sin0^2)
end
B(p,p)=A(p,p)*cos0^2+A(q,q)*sin0^2-2*A(p,q)*sin0*cos0
B(q,q)=A(p,p)*sin0^2+A(q,q)*cos0^2+2*A(p,q)*sin0*cos0
B(p,q)=(A(p,p)-A(q,q))*sin0*cos0+A(p,q)*(cos0^2-sin0^2)
S(i,i)=S(i,i)
S(i,p)=S(i,p)*cos0-S(i,q)*sin0
S(i,q)=S(i,p)*sin0+S(i,q)*cos0
end
end
end
disp(B,"B =")
disp(S,"S =")
printf('\n\n\nComputation error in the solution provided by book')
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