Optimal expansion of subspaces for eigenvector approximations
نویسندگان
چکیده
منابع مشابه
Galerkin eigenvector approximations
How close are Galerkin eigenvectors to the best approximation available out of the trial subspace? Under a variety of conditions the Galerkin method gives an approximate eigenvector that approaches asymptotically the projection of the exact eigenvector onto the trial subspace—and this occurs more rapidly than the underlying rate of convergence of the approximate eigenvectors. Both orthogonal-Ga...
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Thermal correlation functions C(t) ∼ 〈φ(t)φ(0)〉 in ohmically damped systems such as optical resonators can be expressed as a sum over modes j. In contrast to the conservative case, each term is multiplied by the Petermann factor Cj , which can exceed unity and lead to “excess noise”. A time-independent perturbation ∼ǫ also leads to a response ∼ǫCj . Moreover, C −1 j is proportional to a diagona...
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ژورنال
عنوان ژورنال: Linear Algebra and its Applications
سال: 2008
ISSN: 0024-3795
DOI: 10.1016/j.laa.2007.08.021