منابع مشابه
perturbation series ∗
We discuss certain special cases of algebraic approximants that are given as zeroes of so-called effective characteristic polynomials and their generalization to a multiseries setting. These approximants are useful for the convergence acceleration or summation of quantum mechanical perturbation series. Examples will be given and some properties will be discussed.
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Various perturbation series are factorially divergent. The behavior of their high-order terms can be found by Lipatov’s method, according to which they are determined by instanton configurations of appropriate functional integrals. When the Lipatov asymptotics is known and several lowest order terms of the perturbation series are found by direct calculation of diagrams, one can gain insight int...
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When enumerating trees [1, 2] or prime divisors [3, 4], the leading term of the corresponding asymptotic series is usually sufficient for practical purposes. Greater accuracy is possible by using several more terms, but the coefficients are not as widely known as one might expect. We briefly provide the formulas required to compute the required constants, as well as some theoretical background.
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Asymptotic expansions for a wide class of distribution are studied. Simple method for the computation of the series coefficients is suggested. The case when regularization parameter of distribution depends on the asymptotic parameter is considered.
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Constructing an efficient parametrization of a large, noisy data set of points lying close to a smooth manifold in high dimension remains a fundamental problem. One approach consists in recovering a local parametrization using the local tangent plane. Principal component analysis (PCA) is often the tool of choice, as it returns an optimal basis in the case of noise-free samples from a linear su...
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ژورنال
عنوان ژورنال: Transactions of the American Mathematical Society
سال: 1957
ISSN: 0002-9947
DOI: 10.2307/1992963