Rational Krylov algorithms for nonsymmetric eigenvalue problems. II. matrix pairs
نویسندگان
چکیده
منابع مشابه
Rational Krylov Algorithms for Eigenvalue Computation and Model Reduction
Rational Krylov is an extension of the Lanczos or Arnoldi eigenvalue algorithm where several shifts (matrix factorizations) are performed in one run. A variant has been developed, where these factoriza-tions are performed in parallel. It is shown how Rational Krylov can be used to nd a reduced order model of a large linear dynamical system. In Electrical Engineering, it is important that the re...
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We propose a new uniform framework of Compact Rational Krylov (CORK) methods for solving large-scale nonlinear eigenvalue problems: A(λ)x = 0. For many years, linearizations are used for solving polynomial and rational eigenvalue problems. On the other hand, for the general nonlinear case, A(λ) can first be approximated by a (rational) matrix polynomial and then a convenient linearization is us...
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The Rational Krylov algorithm computes eigenvalues and eigenvectors of a regular not necessarily symmetric matrix pencil. It is a generalization of the shifted and inverted Arnoldi algorithm, where several factorizations with di erent shifts are used in one run. It computes an orthogonal basis and a small Hessenberg pencil. The eigensolution of the Hessenberg pencil approximates the solution of...
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We present two generalisations of the Krylov subspace method, Arnoldi for the purpose of applying them to nite dimensional eigenvalue problems nonlinear in the eigenvalue parameter. The rst method is called nonlinear rational Krylov subspace and approximates and updates the projection of a linearised problem by nesting a one-sided secant method with Arnoldi. The second method, called nonlinear ...
متن کاملInverse eigenvalue problems linked to rational Arnoldi, and rational nonsymmetric Lanczos
Two inverse eigenvalue problems are discussed. First, given the eigenvalues and a weight vector an extended Hessenberg matrix is computed. This matrix represents the recurrences linked to a (rational) Arnoldi inverse problem. It is well-known that the matrix capturing the recurrence coefficients is of Hessenberg form in the standard Arnoldi case. Considering, however, rational functions and adm...
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ژورنال
عنوان ژورنال: Linear Algebra and its Applications
سال: 1994
ISSN: 0024-3795
DOI: 10.1016/0024-3795(94)90492-8