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Thread Subject:
Eig for tridiagonal matrices

Subject: Eig for tridiagonal matrices

From: Andrew Olney

Date: 16 Feb, 2006 10:01:29

Message: 1 of 2

My understanding is that eig uses QR iteration to find eigenvalues.

If my matrix is already tridiagonal, is it faster to use eig
- which is probably optimized
- doesn't assume tridiagonal input

or is it faster to write my own QR iteration
- that does assume tridiagonal input
- but is not optimized

The constraints of my problem are such that I need to find the
eigenvalues and eigenvectors in two separate steps. Additionally, I
need to triangularize the matrix myself.

Subject: Eig for tridiagonal matrices

From: Andrew Olney

Date: 21 Feb, 2006 17:14:27

Message: 2 of 2

Andrew Olney wrote:
>
>
> My understanding is that eig uses QR iteration to find eigenvalues.
>
> If my matrix is already tridiagonal, is it faster to use eig
> - which is probably optimized
> - doesn't assume tridiagonal input
>
> or is it faster to write my own QR iteration
> - that does assume tridiagonal input
> - but is not optimized
>
> The constraints of my problem are such that I need to find the
> eigenvalues and eigenvectors in two separate steps. Additionally, I
> need to triangularize the matrix myself.

The best solution I've found is here

 <http://www.mit.edu/~persson/mltrid/>

which uses the LAPACK subroutine dsteqr

Its orders of magnitude faster and much more memory efficient for
finding just eigenvalues.

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