منابع مشابه
Constructing a Unitary Hessenberg Matrix from Spectral Data
We consider the numerical construction of a unitary Hessenberg matrix from spectral data using an inverse QR algorithm. Any unitary upper Hessenberg matrix H with nonnegative subdiagonal elements can be represented by 2n ? 1 real parameters. This representation, which we refer to as the Schur parameterization of H; facilitates the development of eecient algorithms for this class of matrices. We...
متن کاملAn Efficient QR Algorithm for a Hessenberg Submatrix of a Unitary Matrix
We describe an efficient procedure for implementing the Hessenberg QR algorithm on a class of matrices that we refer to as subunitary matrices. This class includes the set of Szegő-Hessenberg matrices, whose characteristic polynomials are Szegő polynomials, i.e., polynomials orthogonal with respect to a measure on the unit circle in the complex plane. Computing the zeros of Szegő polynomials is...
متن کاملA Solution of Inverse Eigenvalue Problems for Unitary Hessenberg Matrices
Let H ∈ Cn×n be an n × n unitary upper Hessenberg matrix whose subdiagonal elements are all positive. Partition H as H = H11 H12 H21 H22 , (0.1) where H11 is its k×k leading principal submatrix; H22 is the complementary matrix of H11. In this paper, H is constructed uniquely when its eigenvalues and the eigenvalues of b H11 and b H22 are known. Here b H11 and b H22 are rank-one modifications of...
متن کاملOn a Sturm Sequence of Polynomials for Unitary Hessenberg Matrices
Unitary matrices have a rich mathematicalstructure which is closely analogous to real symmetric matrices. For real symmetric matrices this structure can be exploited to develop very eecient numerical algorithms and for some of these algorithms unitary analogues are known. Here we present a unitary analogue of the bisection method for symmetric tridiagonal matrices. Recently Delsarte and Genin i...
متن کاملFamily of solvable generalized random-matrix ensembles with unitary symmetry.
We construct a very general family of characteristic functions describing random matrix ensembles (RME) having a global unitary invariance, and containing an arbitrary, one-variable probability measure, which we characterize by a "spread function." Various choices of the spread function lead to a variety of possible generalized RMEs, which show deviations from the well-known Gaussian RME origin...
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ژورنال
عنوان ژورنال: Linear Algebra and its Applications
سال: 2013
ISSN: 0024-3795
DOI: 10.1016/j.laa.2013.10.008