UKy Wednesday Seminar.

[Satish K. Vanimisetti]

Hi all,

The following is the abstract for tomorrows talk.
As usual we will meet in Lucky Lab tomorrow at 2:30PM Eastern time for
testing.

Thanks
Satish Vanimisetti

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"High Accuracy Algorithms for Computing Eigenvalues of M-matrices"
Qiang Ye
UK Department of Mathematics
Wednesday, September 20, 2000 at 3:30 p.m.

ABSTRACT:  Standard algorithms such as the QR algorithm for computing matrix
eigenvalues are known to be backward stable. This means that the eigenvalues
are computed to the accuracy as warranted by the data.  Then small or
ill-conditioned eigenvalues are only determined to low relative accuracy. In
the last decade, significant advances have been made in identifying the
classes of matrices for which the eigenvalues are determined and can be
computed to high relative accuracy.  In this talk, we present recent
progress on high accuracy computations of the smallest eigenvalue of a
diagonally dominant M-matrix. Using solving quadratic equations as an
example, we shall illustrate when and how the smallest eigenvalue can be
computed to high accuracy.