Results 11 to 20 of about 1,109 (79)
Tridiagonal test matrices for eigenvalue computations : two-parameter extensions of the Clement matrix [PDF]
, 2016 The Clement or Sylvester-Kac matrix is a tridiagonal matrix with zero diagonal and simple integer entries. Its spectrum is known explicitly and consists of integers which makes it a useful test matrix for numerical eigenvalue computations.
Oste, Roy, Van der Jeugt, Joris
core +2 more sources
Improved Cauchy radius for scalar and matrix polynomials [PDF]
, 2017 We improve the Cauchy radius of both scalar and matrix polynomials, which is an upper bound on the moduli of the zeros and eigenvalues, respectively, by using appropriate polynomial multipliers.Comment: 12 ...
Berrington, Janet +12 more
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Perturbed spectra of defective matrices
Journal of Applied Mathematics, Volume 2003, Issue 3, Page 115-140, 2003., 2003 This paper is devoted to the perturbation theory for defective matrices. We consider the asymptotic expansions of the perturbed spectrum when a matrix A is changed to A + tE, where E ≠ 0 and t > 0 is a small parameter. In particular, we analyse the rational exponents that may occur when the matrix E varies over the sphere ‖E‖ = ρ > 0.
Mihail Konstantinov +2 more
wiley +1 more source
Journal of Applied Mathematics, Volume 2003, Issue 9, Page 459-485, 2003., 2003 A comprehensive treatment of Rayleigh‐Schrödinger perturbation theory for the symmetric matrix eigenvalue problem is furnished with emphasis on the degenerate problem. The treatment is simply based upon the Moore‐Penrose pseudoinverse thus distinguishing it from alternative approaches in the literature.
Brian J. McCartin
wiley +1 more source
International Journal of Mathematics and Mathematical Sciences, Volume 25, Issue 6, Page 397-409, 2001., 2001 Solving systems of nonlinear equations and inequalities is of critical importance in many engineering problems. In general, the existence of inequalities in the problem adds to its difficulty. We propose a new projected Hessian Gauss‐Newton algorithm for solving general nonlinear systems of equalities and inequalities.
Mahmoud M. El-Alem +2 more
wiley +1 more source
International Journal of Mathematics and Mathematical Sciences, Volume 28, Issue 5, Page 251-284, 2001., 2001 The systematic analysis of convergence conditions, used in comparison theorems proven for different matrix splittings, is presented. The central idea of this analysis is the scheme of condition implications derived from the properties of regular splittings of a monotone matrix A = M1 − N1 = M2 − N2.
Zbigniew I. Woźnicki
wiley +1 more source
Compression of unitary rank--structured matrices to CMV-like shape with an application to polynomial rootfinding [PDF]
, 2013 This paper is concerned with the reduction of a unitary matrix U to CMV-like shape. A Lanczos--type algorithm is presented which carries out the reduction by computing the block tridiagonal form of the Hermitian part of U, i.e., of the matrix U+U^H.
Bevilacqua, Roberto +2 more
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A fully parallel method for tridiagonal eigenvalue problem
International Journal of Mathematics and Mathematical Sciences, Volume 17, Issue 4, Page 741-752, 1994., 1994 In this paper, a fully parallel method for finding all eigenvalues of a real matrix pencil (A, B) is given, where A and B are real symmetric tridiagonal and B is positive definite. The method is based on the homotopy continuation coupled with the strategy ?Divide‐Conquer? and Laguerre iterations.
Kuiyuan Li
wiley +1 more source
A CMV--based eigensolver for companion matrices [PDF]
, 2014 In this paper we present a novel matrix method for polynomial rootfinding. By exploiting the properties of the QR eigenvalue algorithm applied to a suitable CMV-like form of a companion matrix we design a fast and computationally simple structured QR ...
Bevilacqua, Roberto +2 more
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Bound for the largest singular value of nonnegative rectangular tensors
Open Mathematics, 2016 In this paper, we give a new bound for the largest singular value of nonnegative rectangular tensors when m = n, which is tighter than the bound provided by Yang and Yang in “Singular values of nonnegative rectangular tensors”, Front. Math.
He Jun +4 more
doaj +1 more source