You are currently offline. Some features of the site may not work correctly.

Corpus ID: 10340027

Theorems and counterexamples on structured matrices

@article{Holtz2005TheoremsAC,
title={Theorems and counterexamples on structured matrices},
author={O. Holtz},
journal={arXiv: Rings and Algebras},
year={2005}
}

The subject of Chapter 1 is GKK $\tau$-matrices and related topics. Chapter 2 is devoted to boundedly invertible collections of matrices, with applications to operator norms and spline approximation. Various structured matrices (Toeplitz, Hessenberg, Hankel, Cauchy, and other) are used extensively throughout the thesis.

We will consider three conjectures of Schneider and Varga concerning the location of eigenvalues of ω- and τ-matices in the complex plane, and extend the known results to n ⩽ 4. We will further show… Expand

This paper works on [-1, 1 ] and obtains Markov-type estimates for the derivatives of polynomials from a rather wide family of classes of constrained polynomes and results turn out to be sharp.Expand

It is shown that the size of the entries in the inverse of a band matrix can be bounded in terms of the norm of the matrix, the norm of its inverse and the bandwidth. In many cases this implies that… Expand

We present a conjecture which when true would generalize T. Ando's characterization of the numerical radius of (bounded linear) operators on a Hilbert space (see [A]). Some evidence for the validity… Expand