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in QR decomposition with householder algorithm if matrix A in some state the algorithm will works better and better answer returns

my question is how matrix A should be for householder algorithm to work better

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This question is quite unclear, and the only thing I can think to offer you is that if a matrix is sparse it is better to use Givens reduction instead of Householder. Householder takes half as many operations as Givens though for dense matrices. –  adam W Nov 27 '12 at 20:38
    
to be more clear ... A=QR ok? as you know the QR decomposition not always works according to situation of A ... what is that situation and how A should be to make QR faster and better ... –  Sina Miandashti Nov 28 '12 at 20:36
    
i think if A is upper triangular ... QR is easier and Eigen values of A calculate faster and better ... but unsure and dont know how –  Sina Miandashti Nov 28 '12 at 20:41
    
If $A$ is upper triangular, then $Q=I$ and $R=A$, so no work at all is needed in that case. I believe the only so called failure of QR is when $A$ is singular. –  adam W Nov 29 '12 at 4:07
    
so any possible operation to make A more upper triangular before QR decomposition ? –  Sina Miandashti Nov 29 '12 at 7:32

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