منابع مشابه
Self-similar factor approximants.
The problem of reconstructing functions from their asymptotic expansions in powers of a small variable is addressed by deriving an improved type of approximants. The derivation is based on the self-similar approximation theory, which presents the passage from one approximant to another as the motion realized by a dynamical system with the property of group self-similarity. The derived approxima...
متن کاملMethod of self-similar factor approximants
The method of self-similar factor approximants is completed by defining the approximants of odd orders, constructed from the power series with the largest term of an odd power. It is shown that the method provides good approximations for transcendental functions. In some cases, just a few terms in a power series make it possible to reconstruct a transcendental function exactly. Numerical conver...
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We prove that five well-known identities universally satisfied by commutators in a group generate all universal commutator identities for commutators of weight 4.
متن کاملReconstructing Generalized Exponential Laws by Self-Similar Exponential Approximants
We apply the technique of self-similar exponential approximants based on successive truncations of continued exponentials to reconstruct functional laws of the quasi-exponential class from the knowledge of only a few terms of their power series. Comparison with the standard Padé approximants shows that, in general, the self-similar exponential approximants provide significantly better reconstru...
متن کاملCalculation of critical exponents by self-similar factor approximants
The method of self-similar factor approximants is applied to calculating the critical exponents of the O(N)-symmetric φ4 theory and of the Ising glass. It is demonstrated that this method, being much simpler than other known techniques of series summation in calculating the critical exponents, at the same time, yields the results that are in very good agreement with those of other rather compli...
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ژورنال
عنوان ژورنال: Kyungpook mathematical journal
سال: 2009
ISSN: 1225-6951
DOI: 10.5666/kmj.2009.49.1.001