Results 11 to 20 of about 1,075 (62)
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
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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
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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
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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
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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
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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
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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
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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
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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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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