DM: Re: Why is Singular Vector Decomposition for OLS?

[Warren Sarle]

Krishnadas writes:
> Since SVD is used widely for OLS I guess it has clear advantages 
>over
> plain Inverse(X'X) X'Y.  Can anyone tell me about it?  Any good 
>books
> or references on the motivation for SVD and application of other 
>matrix
> decomposition in statistics?

The main reason to use SVD for OLS is for diagnostics on
ill-conditioning.  SVD is less accurate and much slower than a QR
decomposition. The standard reference is:

   Lawson, C. L. and Hanson, R. J. (1974),
   Solving Least Squares Problems, Englewood Cliffs, NJ:
   Prentice-Hall, Inc. (2nd edition: 1995, Philadelphia: SIAM)

-- 

Warren S. Sarle       SAS Institute Inc.   The opinions expressed here
saswss@unx.sas.com    SAS Campus Drive     are mine and not 
necessarily
(919) 677-8000        Cary, NC 27513, USA  those of SAS Institute.