Eigenvalue precision

Felix_W_ — Tue, 26 Aug 2014 12:51:45 GMT

Hello everyone,

I am working on a project where it is important to distinguish between 0 eigenvalues and non zero eigenvalues. Using the MKL routine LAPACKE_zheev returns me a list of eigenvalues which include some very close to zero. I was wondering what the precision on those is or rather whether they can be reliably distinguished from a zero eigenvalue by the algorithm.

The only thing I have found on this topic so far is an article in the LAPACK specifications on Error bounds:

http://www.netlib.org/lapack/lug/node89.html

Does this article apply to the MKL routines aswell? I.e. is an eigenvalue larger than EERRBD guaranteed to belong to a non zero true eigenvalue? Is there a MKL routine that can be called to get the errorbound?

If anyone has information on this thanks in advance.

The precision on the returned

Zhang_Z_Intel — Tue, 26 Aug 2014 16:45:56 GMT

The precision on the returned eigenvalues from LAPACKE_zheev is "double precision".

The error bounds of the results depend on both machine epsilon and the input matrix. There is a code sample right on the netlib page that you referenced showing exactly how to compute the error bounds.

topic The precision on the returned in Intel® oneAPI Math Kernel Library

Eigenvalue precision

The precision on the returned