MAGMA Forum

I am trying to link together an eigenvector solver using MAGMA functions, using this standard method:

a symmetric matrix is converted to tridiagonal form
matrix goes through QL transformation
eigenvalues are found, eigenvectors found through reverse iteration (code?), eigenvectors are converted back by the tridiagonal transform in reverse

In my understanding, this would require magma SQEHRD\DGEHRD for the hessenberg form,
followed by SQEQLF/DQEQLF for QL transformation

Do you have sources available for these routines? Am I missing a few steps? Any beta eigenvector codes would also be greatly appreciated.

Best,

Matt Slezak

A Hessenberg reduction is not a tridiagonal reduction. One is used to prepare general matrices (Hessenberg) and one is used to prepare symmetric matrices (tridiagonal) for the iterative QR (or less popularly, QL) method.

So what is the tridiagonal code called for symmetric matrices?

Hessenburg creates a tridiagonal form on a symmetric matrix, it just isn't as efficient as the method you mentioned.

Any reverse iteration GPU codes out there for eigenvectors by the way?

Best,

Matt