The implicitly shifted (bulge chasing) QZ algorithm is the most popular method for solving the generalized eigenvalue problem Av = Bv. This paper explains why the QZ algorithm functions well even in the presence of innnite eigenvalues. The key to rapid convergence of QZ (and QR) algorithms is the eeective transmission of shifts during the bulge chase. In this paper the mechanism of transmission...

In recent years, there has been a growing interest in companion matrices. Sparse matrices are well known: every sparse matrix is equivalent to Hessenberg of particular simple type. Recently, Deaett et al. [Electron. J. Linear Algebra, 35:223--247, 2019] started the systematic study nonsparse They proved that nonderogatory, although not necessarily matrix. this paper, which unit described. matri...

Abstract We study the relation between certain non-degenerate lower Hessenberg infinite matrices $${\mathcal {G}}$$ G and existence of sequences orthogonal polynomials with respect to Sobolev inner products. In other words, we extend well-known Favard theorem for orthogonality. characterize structure matrix a...

Abstract We present an approximation for the stationary distribution T of a countably infinite-state Markov chain with transition probability matrix P = (pq) of upper Hessenberg form. Our approximation makes use of an associated upper Hessenberg matrix which is spatially homogeneous one P ( ~ ) except for a finite number of rows obtained by letting p q = pj-i+l, i > N + 1, for some distribution...