Approximation by analytic matrix functions. The four block problem

Details Approximation by analytic matrix functions. The four block problem Approximation by analytic matrix functions. The four block problem

1995-12-22

arxiv.org/abs/math/9512223v1

Mathematics

Classical Analysis and ODEs

Scientific paper

We study the problem of finding a superoptimal solution to the four block problem. Given a bounded block matrix function $\left(\begin{array}{cc}\Phi_{11} &\Phi_{12}\\\Phi_{21}&\Phi_{22}\end{array}\right)$ on the unit circle the four block problem is to minimize the $L^\infty$ norm of $\left(\begin{array}{cc} \Phi_{11}-F&\Phi_{12}\\\Phi_{21}&\Phi_{22}\end{array}\right)$ over $F\in H^\infty$. Such a minimizing $F$ (an optimal solution) is almost never unique. We consider the problem to find a superoptimal solution which minimizes not only the supremum of the matrix norms but also the suprema of all further singular values. We give a natural condition under which the superoptimal solution is unique.

Affiliated with

Also associated with

No associations

Rating

Approximation by analytic matrix functions. The four block problem does not yet have a rating. At this time, there are no reviews or comments for this scientific paper.

If you have personal experience with Approximation by analytic matrix functions. The four block problem, we encourage you to share that experience with our LandOfFree.com community. Your opinion is very important and Approximation by analytic matrix functions. The four block problem will most certainly appreciate the feedback.

Rate now

Comments { 0 }

Profile ID: LFWR-SCP-O-621491