%Household变化QR分解数值求问题 -Laplace u=lambda*u（ 边界上为0）差分离散后的特征值
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%一维
N=17;%剖分数，中间节点个数N-1
d=1;
h=pi/N;
A=zeros(N-1,N-1);
for i=1:N-1
A(i,i)=2;
end
for i=2:N-1
A(i-1,i)=-1;
A(i,i-1)=-1;
end
A=A/h^2;
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% %二维
% N=5;%一个方向上的剖分数，中间节点个数(N-1)^2
% d=2;
% h=pi/N;
% A=zeros((N-1)^2,(N-1)^2);
% A1=zeros(N-1,N-1);
% for i=1:N-1
% A1(i,i)=4;
% end
% for i=2:N-1
% A1(i-1,i)=-1;
% A1(i,i-1)=-1;
% end
% for i=1:N-1
% A((i-1)*(N-1)+1:i*(N-1),(i-1)*(N-1)+1:i*(N-1))=A1;
% end
% for i=1:N-2
% A((i-1)*(N-1)+N:(i+1)*(N-1),(i-1)*(N-1)+1:i*(N-1))=-eye(N-1,N-1);
% A((i-1)*(N-1)+1:i*(N-1),(i-1)*(N-1)+N:(i+1)*(N-1))=-eye(N-1,N-1);
% end
% A=A/h^2;
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[V,D] = eig(A);
diag(D)
for j=1:50 %迭代次数可改变
Q=eye((N-1)^d,(N-1)^d);
for i=1:(N-1)^d-1
R=Hxkj(A(:,i),i,(N-1)^d);
A=R*A;
Q=Q*R';
end
A=A*Q;
end
lambda=diag(A)
