QR and permutation matrix
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10-26-2015, 07:24 PM
Post: #4
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RE: QR and permutation matrix
(10-26-2015 05:04 PM)parisse Wrote: There is indeed no need to have a permutation matrix, you can check that in giac in vecteur.cc in qr_ortho, the idn matrix is here for compatibility. There is pivoting in the sense that to reduce a given column the line with highest absolute value is choosen. I am not sure what you mean by this. If \[ A = \begin{bmatrix} a_{1} & a_{2} & \dotsm & a_{n} \\ \end{bmatrix} \] then the first step is to swap columns (if necessary) so that the column column \( a_1 \) is replaced with the column having largest norm? And then a Householder reflection is applied? (And similarly for submatrices) Is that what you meant by pivoting? Quote:Can you explain what is the reason behind having a permutation matrix? QR factorization with pivoting gives R with diagonal terms in non-decreasing order. This is useful for factoring rank-deficient matrices. Graph 3D | QPI | SolveSys |
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Messages In This Thread |
QR and permutation matrix - Han - 10-26-2015, 03:04 PM
RE: QR and permutation matrix - parisse - 10-26-2015, 05:04 PM
RE: QR and permutation matrix - Han - 10-26-2015 07:24 PM
RE: QR and permutation matrix - Han - 10-26-2015, 05:16 PM
RE: QR and permutation matrix - parisse - 10-27-2015, 06:48 AM
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