B. Laszkiewicz, K. Ziêtak, 

Approximation by matrices with restricted spectra, 
Linear Algebra nad Its Applications 428 (2008), 1031-1040.


We investigate the properties of the approximation of a matrix by matrices whose spectra 
are in a closed convex set of the complex plane. We explain why the Khalil and Maher 
characterization of an approximant, which spectrum is in a strip, is not quite correct. 
We prove that their characterization is valid but for another kind of approximation. 
We formulate a conjecture which leads to some algorithm for computing approximants. 
The conjecture is motivated by numerical experiments and some theoretical considerations. 
Separately we consider the approximation of normal matrices.



Key words:  Approximation of matrices; Restricted spectrum; Halmos approximant