Many practical problems in elasticity, vibration, etc., when modeled
mathematically, reduce to the matrix eigenvalue problem. Rounding errors
severely limit the accuracy of the computed eigenvalues the conventional
matrix algorithms (e.g., the ones employed by MATLAB) usually compute only
the largest eigenvalues accurately. The tiny ones are lost to roundoff
even though often they are accurately determined by the data and of most
physical significance.
In this talk, we present a survey of recent work of the author
and his collaborators on good distribution of points on a class of
rectifiable sets including the sphere. We will also present some
interesting applications of our work to imaging, combinatorics and
numerical integration with the aim of finding new applications and
collaborations. The talk will be easy to follow and undergraduate and
graduate students are welcome to attend.
