In recent years several new classes of matrices have been discovered and their structure
exploited to design fast and accurate algorithms. In this new reference work, Raf Vandebril …

Currently there is a growing interest in semiseparable matrices and generalized
semiseparable matrices. To gain an appreciation of the historical evolution of this concept …

The QR-algorithm is a renowned method for computing all eigenvalues of an arbitrary
matrix. A preliminary unitary similarity transformation to Hessenberg form is indispensable …

In this paper, we survey several recent results that highlight an interplay between a relatively
new class of quasiseparable matrices and univariate polynomials. Quasiseparable matrices …

The QR algorithm is one of the classical methods to compute the eigendecomposition of a
matrix. If it is applied on a dense n× n matrix, this algorithm requires O (n3) operations per …

For an n*n tridiagonal matrix we exploit the structure of its QR factorization to devise two new
algorithms for computing the 1-norm condition number in O(n) operations. The algorithms …

In this paper we describe an orthogonal similarity transformation for transforming arbitrary
symmetric matrices into a diagonal-plus-semiseparable matrix, where we can freely choose …

In the last few years many numerical techniques for computing eigenvalues of structured
rank matrices have been proposed. Most of them are based on QR iterations since, in the …

In this paper we show how to perform in an explicit way the shifted QR-algorithm for
computing the eigenvalues of a rank structured matrix. The implementation is based on the …

In this paper, we will derive a solver for a symmetric strongly nonsingular higher order
generator representable semiseparable plus band matrix. The solver we will derive is based …