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Simplification of the Gram Matrix Eigenvalue Problem for Quadrature Amplitude Modulation Signals [PDF]
Entropy, 2022 In quantum information science, it is very important to solve the eigenvalue problem of the Gram matrix for quantum signals. This allows various quantities to be calculated, such as the error probability, mutual information, channel capacity, and the ...
Ryusuke Miyazaki +2 more
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Multiple-rank modification of symmetric eigenvalue problem [PDF]
MethodsX, 2018 Rank-1 modifications applied k-times (k > 1) often are performed to achieve a rank-k modification. We propose a rank- k modification for enhancing computational efficiency. As the first step toward a rank- k modification, an algorithm to perform a rank-2
HyungSeon Oh, Zhe Hu
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The Quadratic Eigenvalue Problem [PDF]
SIAM Review, 2001 The authors review current knowledge of the matrix quadratic eigenvalue problem, \[ (\lambda ^2 M+\lambda C+K)x=0, \qquad y^* (\lambda ^2 M+\lambda C+K)=0, \tag{1} \] including its main applications and its numerical solution, and give an excellent guide to the literature.
Françoise Tisseur, Karl Meerbergen
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THE HYPERBOLIC QUADRATIC EIGENVALUE PROBLEM [PDF]
Forum of Mathematics, Sigma, 2015 The hyperbolic quadratic eigenvalue problem (HQEP) was shown to admit Courant–Fischer type min–max principles in 1955 by Duffin and Cauchy type interlacing inequalities in 2010 by Veselić.
XIN LIANG, REN-CANG LI
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Guaranteed Eigenvalue Bounds for the Steklov Eigenvalue Problem [PDF]
SIAM Journal on Numerical Analysis, 2019 To provide mathematically rigorous eigenvalue bounds for the Steklov eigenvalue problem, an enhanced version of the eigenvalue estimation algorithm developed by the third author is proposed, which removes the requirements of the positive definiteness of bilinear forms in the formulation of eigenvalue problems.
Hehu Xie, Xuefeng Liu
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The octonionic eigenvalue problem
Advances in Applied Clifford Algebras, 1998 plain TeX (uses AMS fonts), 18 pages, 1 PS figure included with ...
Manogue Corinne A, Dray Tevian
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Nonlinear Eigenvalue Problems with Specified Eigenvalues [PDF]
SIAM Journal on Matrix Analysis and Applications, 2014 This work considers eigenvalue problems that are nonlinear in the eigenvalue parameter. Given such a nonlinear eigenvalue problem T, we are concerned with finding the minimal backward error such that T has a set of prescribed eigenvalues with prescribed algebraic multiplicities.
Michael Karow +2 more
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Generalized eigenvalue problems with specified eigenvalues [PDF]
IMA Journal of Numerical Analysis, 2013 We consider the distance from a (square or rectangular) matrix pencil to the nearest matrix pencil in 2-norm that has a set of specified eigenvalues. We derive a singular value optimization characterization for this problem and illustrate its usefulness for two applications.
D. Kressner +3 more
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Rectangular eigenvalue problems
Advances in Computational Mathematics, 2022 AbstractOften the easiest way to discretize an ordinary or partial differential equation is by a rectangular numerical method, in which n basis functions are sampled at m ≫ n collocation points. We show how eigenvalue problems can be solved in this setting by QR reduction to square matrix generalized eigenvalue problems.
Hashemi, B +2 more
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A constrained eigenvalue problem [PDF]
Linear Algebra and its Applications, 1989 For the problem of finding \(Min(x^ TAx)\) for a symmetric matrix A subject to \(x^ Tx=1\) and \(N^ Tx=t\) theoretical and numerical methods are described. First the linear constraint is removed and then Lagrange multipliers are employed reducing the problem to solve either a secular equation or a quadratic eigenvalue problem.
Gander, Walter +2 more
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