Adaptive Rational Interpolation: Arnoldi and Lanczos-like Equations
نویسندگان
چکیده
منابع مشابه
Adaptive Rational Interpolation: Arnoldi and Lanczos-like Equations
The Arnoldi and Lanczos algorithms, which belong to the class of Krylov subspace methods, are increasingly used for model reduction of large scale systems. The standard versions of the algorithms tend to create reduced order models that poorly approximate low frequency dynamics. Rational Arnoldi and Lanczos algorithms produce reduced models that approximate dynamics at various frequencies. This...
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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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The GMRES and Arnoldi algorithms, which reduce to the CR and Lanczos algorithms in the symmetric case, both minimize p(A)b over polynomials p of degree n. The difference is that p is normalized at z 0 for GMRES and at z x for Arnoldi. Analogous "ideal GMRES" and "ideal Arnoldi" problems are obtained if one removes b from the discussion and minimizes p(/l)II instead. Investigation of these true ...
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Since version 2.4 of the RKToolbox, the rat krylov function can simulate the parallel construction of a rational Krylov basis. This is done by imposing various nonzero patterns in a so-called continuation matrix T . Simply speaking, the j-th column of this matrix contains the coefficients of the linear combination of j rational Krylov basis vectors which have been used to compute the next (j + ...
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This report provides an introductory overview of the numerical solution of large scale algebraic eigenvalue problems. The main focus is on a class of methods called Krylov subspace projection methods. The Lanczos method is the premier member of this class and the Arnoldi method is a generalization to the nonsymmetric case. A recently developed and very promising variant of the Arnoldi/Lanczos s...
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ژورنال
عنوان ژورنال: European Journal of Control
سال: 2008
ISSN: 0947-3580
DOI: 10.3166/ejc.14.342-354