Noda iterations for generalized eigenproblems following Perron-Frobenius theory
Sign Up to like & getrecommendations! Published in 2018 at "Numerical Algorithms"
DOI: 10.1007/s11075-018-0512-4
Abstract: In this paper, we investigate the generalized eigenvalue problem Ax = λBx arising from economic models. Under certain conditions, there is a simple generalized eigenvalue ρ(A, B) in the interval (0, 1) with a positive… read more here.
Keywords: generalized eigenproblems; generalized eigenvalue; noda iterations; noda iteration ... See more keywords
R type recurrence, generalized eigenvalue problem and orthogonal polynomials on the unit circle
Sign Up to like & getrecommendations! Published in 2019 at "Linear Algebra and its Applications"
DOI: 10.1016/j.laa.2018.10.005
Abstract: We consider a sequence of polynomials $\{P_n\}_{n \geq 0}$ satisfying a special $R_{II}$ type recurrence relation where the zeros of $P_n$ are simple and lie on the real line. It turns out that the polynomial… read more here.
Keywords: type recurrence; unit circle; eigenvalue problem; recurrence ... See more keywords
Simple yet effective analysis of waveguide mode symmetry: generalized eigenvalue approach based on Maxwell's equations.
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DOI: 10.1364/oe.472148
Abstract: Particular waveguide structures and refractive index distribution can lead to specified degeneracy of eigenmodes. To obtain an accurate understanding of this phenomenon, we propose a simple yet effective approach, i.e., generalized eigenvalue approach based on… read more here.
Keywords: yet effective; maxwell equations; generalized eigenvalue; symmetry ... See more keywords
A Shift-Deflation Technique for Computing a Large Quantity of Eigenpairs of the Generalized Eigenvalue Problems
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DOI: 10.3390/sym14122547
Abstract: In this paper, we propose a shift-deflation technique for the generalized eigenvalue problems. This technique consists of the following two stages: the shift of converged eigenvalues to zeros, and the deflation of these shifted eigenvalues.… read more here.
Keywords: shift deflation; eigenvalue problems; generalized eigenvalue; deflation technique ... See more keywords
The Numerical Solution of Large-Scale Generalized Eigenvalue Problems Arising from Finite-Element Modeling of Electroelastic Materials
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DOI: 10.3390/sym15010171
Abstract: The generalized eigenvalue problem for a symmetric definite matrix pencil obtained from finite-element modeling of electroelastic materials is solved numerically by the Lanczos algorithm. The mass matrix is singular in the considered problem, and therefore… read more here.
Keywords: modeling electroelastic; finite element; element modeling; generalized eigenvalue ... See more keywords