A Rational Krylov Method Based on Hermite Interpolation for Nonlinear Eigenvalue Problems
نویسندگان
چکیده
منابع مشابه
A Rational Krylov Method Based on Hermite Interpolation for Nonlinear Eigenvalue Problems
This paper proposes a new rational Krylov method for solving the nonlinear eigenvalue problem (NLEP): A(λ)x = 0. The method approximates A(λ) by Hermite interpolation where the degree of the interpolating polynomial and the interpolation points are not fixed in advance. It uses a companion-type reformulation to obtain a linear generalized eigenvalue problem (GEP). To this GEP we apply a rationa...
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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: SIAM Journal on Scientific Computing
سال: 2013
ISSN: 1064-8275,1095-7197
DOI: 10.1137/120877556