Herbert H. H. Homeier

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A nonlinear sequence transformation is presented which is able to accelerate the convergence of Fourier series. It is tailored to be exact for a certain model sequence. As in the case of the Levin transformation and other transformations of Levin-type, in this model sequence the partial sum of the series is written as the sum of the limit (or antilimit) and(More)
Sequence transformations are important tools for the convergence acceleration of slowly convergent scalar sequences or series and for the summation of divergent series. The basic idea is to construct from a given sequence { {sn} } a new sequence { {s ′ n } } = T ({ {sn} }) where each s ′ n depends on a finite number of elements sn 1 ,. .. , sn m. Often, the(More)
Recently, the author proposed a new nonlinear sequence transformation, the iterative $$J$$ transformation, which was shown to provide excellent results in several applications (Homeier [15]). In the present contribution, this sequence transformation is derived by a hierarchically consistent iteration of some basic transformation. Hierarchical consistency is(More)
A new nonlinear sequence transformation, the iterative J transformation, was proposed recently For this transformation, a derivation based on the method of hierarchical consistency, alternative recursive representations, general properties, an explicit expression for the kernel, model sequences, and its relation to other sequence transformations have been(More)
We derive the I transformation, an iterative sequence transformation that is useful for the convergence acceleration of certain Fourier series. The derivation is based on the concept of hierarchical consistency in the asymptotic regime. We show that this sequence transformation is a special case of the J transformation. Thus, many properties of the I(More)
Recently, Sidi [Sidi, A. (1995): Acceleration of convergence of (generalized) Fourier series by the d-transformation. Ann. Numer. Math. 2, 381–406] proposed a method for the convergence acceleration of certain orthogonal expansions. The present contribution shows that it is possible to extend the method proposed by Sidi to a wider class of problems by(More)
The solution of the Ornstein-Zernike equation with various closure approximations is studied. This problem is rewritten as an integral equation that can be solved iteratively on a grid. The convergence of the xed point iterations is relatively slow. We consider transformations of the sequence of solution vectors using non-linear sequence transformations,(More)