[
https://issues.apache.org/jira/browse/MAHOUT-45?page=com.atlassian.jira.plugin.system.issuetabpanels:comment-tabpanel&focusedCommentId=12590608#action_12590608
]
Ted Dunning commented on MAHOUT-45:
-----------------------------------
The numerical instability of GS is due to loss of orthogonality, not so much
errors in normalization.
Householder and Givens approaches are about equal AFAIK, but the wikipedia
article claims Givens is easier to parallelize. I am not sure that applies for
Map-Reduce. Givens is definitely easier to apply in a sparse case since you
don't have to deal with an entire (mostly zero) row or column at a time.
Golub and van Loan, p 219 (2nd edition) has a discussion that shows that the
error for *modified* Gram-Schmidt is about k u where k is the condition number
of the matrix and u is a single ULP while Householder and Givens approaches
have error about the same as u. This implies that hilbert matrices might be
good test cases.
> Matrix QR decomposition
> -----------------------
>
> Key: MAHOUT-45
> URL: https://issues.apache.org/jira/browse/MAHOUT-45
> Project: Mahout
> Issue Type: Improvement
> Components: Matrix
> Reporter: Sergey Chickin
> Priority: Minor
> Attachments: MAHOUT-45.patch
>
>
> Matrix QR decomposition and appropriate determinant calculator
--
This message is automatically generated by JIRA.
-
You can reply to this email to add a comment to the issue online.
