Add support for SVD.
--------------------
Key: MATH-157
URL: http://issues.apache.org/jira/browse/MATH-157
Project: Commons Math
Issue Type: New Feature
Reporter: Tyler Ward
SVD is probably the most important feature in any linear algebra package,
though also one of the more difficult.
In general, SVD is needed because very often real systems end up being singular
(which can be handled by QR), or nearly singular (which can't). A good example
is a nonlinear root finder. Often the jacobian will be nearly singular, but it
is VERY rare for it to be exactly singular. Consequently, LU or QR produces
really bad results, because they are dominated by rounding error. What is
needed is a way to throw out the insignificant parts of the solution, and take
what improvements we can get. That is what SVD provides. The colt SVD algorithm
has a serious infinite loop bug, caused primarily by Double.NaN in the inputs,
but also by underflow and overflow, which really can't be prevented.
If worried about patents and such, SVD can be derrived from first principals
very easily with the acceptance of two postulates.
1) That an SVD always exists.
2) That Jacobi reduction works.
Both are very basic results from linear algebra, available in nearly any text
book. Once that's accepted, then the rest of the algorithm falls into place in
a very simple manner.
--
This message is automatically generated by JIRA.
-
If you think it was sent incorrectly contact one of the administrators:
http://issues.apache.org/jira/secure/Administrators.jspa
-
For more information on JIRA, see: http://www.atlassian.com/software/jira
---------------------------------------------------------------------
To unsubscribe, e-mail: [EMAIL PROTECTED]
For additional commands, e-mail: [EMAIL PROTECTED]
