Problem with Upper Hessenberg Reduction

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Daniela Valdés 2015-1-31

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https://ww2.mathworks.cn/matlabcentral/answers/173996-problem-with-upper-hessenberg-reduction

评论： hemanth vemuluri 2021-1-9

Hello. I'm having trouble with the algorithm of the reduction to the Upper Hessenberg form through Householder reflections. Here it's what I have so far:

function [Q,H]=Hessenbergsup(A,p)
[m,n]=size(A)
Q=eye(n)
if m!=n
  disp("A isn't a square matrix")
else
  if p==1 # Householder Reflections
    H=A
    for k=1:(n-2)
      x=H((k+1):n,k)
      u=((sign(x(1)))*(norm(x,2))*eye((n-k),k)) + x
      u=u/((norm(u,2))^2)
      H(k+1:n,k:n)=H(k+1:n,k:n)-2*u*((u')*(H(k+1:n,k:n)))
      H(1:n,(k+1):n)=H(1:n,(k+1):n)-2*((H(1:n,(k+1):n))*u)*(u')
      Q(1:n,(k+1):n)=Q(1:n,(k+1):n)-2*((Q(1:n,(k+1):n))*u)*(u')
    endfor
  endif
  if p==2 # Arnoldi Iterations (not done yet)
  endif
endif
end