منابع مشابه
A Nonlinear Eigenvalue Problem
My lectures at the Minicorsi di Analisi Matematica at Padova in June 2000 are written up in these notes1. They are an updated and extended version of my lectures [37] at Jyväskylä in October 1994. In particular, an account of the exciting recent development of the asymptotic case is included, which is called the ∞-eigenvalue problem. I wish to thank the University of Padova for financial suppor...
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The Arnoldi method for standard eigenvalue problems possesses several attractive properties making it robust, reliable and efficient for many problems. Our first important result is a characterization of a general nonlinear eigenvalue problem (NEP) as a standard but infinite dimensional eigenvalue problem involving an integration operator denoted B. In this paper we present a new algorithm equi...
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An estimate for the spectrum of the two-dimensional eigenvalue problem Am + Xe" = 0 in D (X > 0), u = 0 on 3 D is derived, and upper and lower pointwise bounds for the solutions are constructed. 1. Let D be a simply connected bounded domain in the plane with a piecewise analytic boundary 3D. Consider the nonlinear Dirichlet problem Am(x) + Xe"w = 0 in D, (1) u(x) = 0 on dD, where X is a positiv...
متن کاملOn an Eigenvector-Dependent Nonlinear Eigenvalue Problem
We first provide existence and uniqueness conditions for the solvability of an algebraic eigenvalue problem with eigenvector nonlinearity. We then present a local and global convergence analysis for a self-consistent field (SCF) iteration for solving the problem. The well-known sin Θ theorem in the perturbation theory of Hermitian matrices plays a central role. The near-optimality of the local ...
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We present a new framework of Compact Rational Krylov (CORK) methods for solving the nonlinear eigenvalue problem (NLEP): A(λ)x = 0, where λ ∈ Ω ⊆ C is called an eigenvalue, x ∈ Cn \ {0} the corresponding eigenvector, and A : Ω→ Cn×n is analytic on Ω. Linearizations are used for many years for solving polynomial eigenvalue problems [5]. The matrix polynomial P (λ) = ∑d i=0 λ Pi, with Pi ∈ Cn×n,...
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ژورنال
عنوان ژورنال: Acta Numerica
سال: 2017
ISSN: 0962-4929,1474-0508
DOI: 10.1017/s0962492917000034