The Parrott problem for singular values
David Ogle and Nicholas Young
Status
Appeared in the proceedings of the 1998 IWOTA conference
in Groningen, Operator Theory: Advances and Applications Vol. 124,
Birkhauser, 2001.
Abstract
We discuss the problem of completing a partially specified matrix $\left[
\begin{array}{cc} A & B \\ C & ? \end{array} \right]$ subject to a bound
on the $m$th singular value.
A complete solution was given by Arsene, Constantinescu, and Gheondea.
We present a more elementary approach appropriate to the matrix case based
on the use of M\"{o}bius transformations.
D.J. Ogle's work was supported by an EPSRC grant;
this work was also supported by NATO Collaborative grant CRG 971129
Nicholas Young
06 May 1999.