Jacobians and rank 1 perturbations relating to unitary Hessenberg matrices
نویسندگان
چکیده
منابع مشابه
5 M ay 2 00 5 Jacobians and rank 1 perturbations relating to unitary Hessenberg matrices
In a recent work Killip and Nenciu gave random recurrences for the characteristic polynomials of certain unitary and real orthogonal upper Hessenberg matrices. The corresponding eigenvalue p.d.f.’s are β-generalizations of the classical groups. Left open was the direct calculation of certain Jacobians. We provide the sought direct calculation. Furthermore, we show how a multiplicative rank 1 pe...
متن کاملUnitary rank structured matrices
In this paper we describe how one can represent a unitary rank structured matrix in an efficient way as a product of unitary or Givens transformations. We provide also some basic operations for manipulating the representation, such as the transition to zerocreating form, the transition to a unitary/Givens-weight representation, as well as an internal pull-through process of the two branches of ...
متن کاملSimilarity of perturbations of Hessenberg matrices
To every infinite lower Hessenberg matrix D is associated a linear operator on l2. In this paper we prove the similarity of the operator D − ∆, where ∆ belongs to a certain class of compact operators, to the operator D−∆′, where ∆′ is of rank one. We first consider the case when ∆ is lower triangular and has finite rank; then we extend this to ∆ of infinite rank assuming that D is bounded. In S...
متن کاملPolynomial perturbations of bilinear functionals and Hessenberg matrices
This paper deals with symmetric and non-symmetric polynomial perturbations of symmetric quasi-de nite bilinear functionals. We establish a relation between the Hessenberg matrices associated with the initial and the perturbed functionals using LU and QR factorizations. Moreover we give an explicit algebraic relation between the sequences of orthogonal polynomials associated with both functionals.
متن کاملConvergence of the shifted QR algorithm for unitary Hessenberg matrices
This paper shows that for unitary Hessenberg matrices the QR algorithm, with (an exceptional initial-value modification of) the Wilkinson shift, gives global convergence; moreover, the asymptotic rate of convergence is at least cubic, higher than that which can be shown to be quadratic only for Hermitian tridiagonal matrices, under no further assumption. A general mixed shift strategy with glob...
متن کاملذخیره در منابع من
با ذخیره ی این منبع در منابع من، دسترسی به آن را برای استفاده های بعدی آسان تر کنید
ژورنال
عنوان ژورنال: International Mathematics Research Notices
سال: 2006
ISSN: 1073-7928,1687-0247
DOI: 10.1155/imrn/2006/48306