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From "Ted Dunning (JIRA)" <j...@apache.org>
Subject [jira] Commented: (MAHOUT-45) Matrix QR decomposition
Date Fri, 18 Apr 2008 20:40:21 GMT

    [ 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

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