[SciPy-User] eigenvalues of a symmetric tridiagonal matrix

[nicky van foreest]

Hi Robert,

The answer is perhaps a bit off-topic for the scipy community.

For your matrix it is easy to write the characteristic polynomial (the
polynomial whose roots give the eigenvalues of the matrix) in a
recursive way. This property should enable you to find the eigenvalues
very fast and accurately (it can be proven that the eigenvalues
satisfy all kinds of nice properties. If you are interested, check the
home page of Erik van Doorn at Twente University. The sequence of
characteristic polynomial forms a sequence of Sturm polynomials.)

Hope this helps somewhat.

Nicky

On 23 February 2011 15:02, Robert Cimrman <cimrman3 at ntc.zcu.cz> wrote:
> Hi,
>
> does anybody know about a Python code for computing some (e.g. the
> smallest) eigenvalues of a symmetric tridiagonal matrix?
>
> I can reasonably get what I need using scipy.linalg.eigvals_banded(), but
> wonder if there is something even more efficient.
>
> In lapack, there are sstebz, dstebz functions, but they seem not to be
> wrapped in scipy - the following returns nothing:
>
> import scipy.lib.lapack as ll
> ll.get_lapack_funcs(['stebz'])
>
> Also, does anyone have experience with [1]?
>
> Thanks,
> r.
>
> [1] http://kochanski.org/gpk/misc/PyLapack.html
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