Root class TDecompQRH - how to use |
original | comment / corrected version |
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Decompose an (m x n)-matrix A with m ≥ n. | ok |
A = QRH | A = QR
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Q : orthogonal (m x n) - matrix, stored in fQ; | Everything wrong! "Orthogonal" - yes, but :
![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() Now we can describe what does fQ contain?
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R : upper triangular (n x n)-matrix, stored in fR; | It is found as ![]() ![]() ![]() First, R is computed and placed into upper part of fQ, then copied into fR |
H : (n x n)-Householder matrix, stored through; | The H matrix is a nonsence: as we see, the involved matrices are ![]() ![]() |
fUp : n-vector with Householder up‘s; | Correct if one deciphers the "Householder up‘s" as upper components of Householder vectors ![]() ![]() |
fW : n-vector with Householder beta‘s. | Similarly, an explicit definition is much better: ![]() |
The decomposition fails if in the formation of reflectors a zero appears, i.e. singularity. | ? (I did not check this statement) |
I | Attachment | History | Action | Size | Date | Who | Comment |
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Golub_VanLoan.Matr_comp_2ed_ru.djvu | r1 | manage | 7867.5 K | 2011-05-02 - 04:37 | AlexanderFedotov | |
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Golub_VanLoan.Matr_comp_3ed.pdf | r1 | manage | 11833.8 K | 2011-05-02 - 04:25 | AlexanderFedotov | |
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QRH_userguide526.gif | r1 | manage | 15.3 K | 2011-05-03 - 20:05 | AlexanderFedotov |