Results 11 to 20 of about 1,086 (62)
A note on certain ergodicity coeflcients
Special Matrices, 2015 We investigate two ergodicity coefficients ɸ ∥∥ and τn−1, originally introduced to bound the subdominant eigenvalues of nonnegative matrices. The former has been generalized to complex matrices in recent years and several properties for such generalized ...
Tudisco Francesco
doaj +4 more sources
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
core +2 more sources
The calculation of the distance to a nearby defective matrix [PDF]
, 2012 In this paper a new fast algorithm for the computation of the distance of a matrix to a nearby defective matrix is presented. The problem is formulated following Alam & Bora (Linear Algebra Appl., 396 (2005), pp.~273--301) and reduces to finding when a ...
Freitag, Melina A., Spence, Alastair
core +1 more source
On the Yang-Baxter-like matrix equation for rank-two matrices
Open Mathematics, 2017 Let A = PQT, where P and Q are two n × 2 complex matrices of full column rank such that QTP is singular. We solve the quadratic matrix equation AXA = XAX.
Zhou Duanmei, Chen Guoliang, Ding Jiu
doaj +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
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
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
core +2 more sources
Rayleigh-Ritz Majorization Error Bounds for the Linear Response Eigenvalue Problem
Open Mathematics, 2019 In the linear response eigenvalue problem arising from computational quantum chemistry and physics, one needs to compute a few of smallest positive eigenvalues together with the corresponding eigenvectors.
Teng Zhongming, Zhong Hong-Xiu
doaj +1 more source
Block Tridiagonal Reduction of Perturbed Normal and Rank Structured Matrices [PDF]
, 2013 It is well known that if a matrix $A\in\mathbb C^{n\times n}$ solves the matrix equation $f(A,A^H)=0$, where $f(x, y)$ is a linear bivariate polynomial, then $A$ is normal; $A$ and $A^H$ can be simultaneously reduced in a finite number of operations to ...
Bevilacqua, Roberto +2 more
core +3 more sources
A Geršgorin-type eigenvalue localization set with n parameters for stochastic matrices
Open Mathematics, 2018 A set in the complex plane which involves n parameters in [0, 1] is given to localize all eigenvalues different from 1 for stochastic matrices. As an application of this set, an upper bound for the moduli of the subdominant eigenvalues of a stochastic ...
Wang Xiaoxiao, Li Chaoqian, Li Yaotang
doaj +1 more source