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 constructâ€¦ (More)

Remainder estimates for Levin-type sequence transformations are discussed. A new remainder estimate is introduced which is related to the Kummer transformation. Test cases are presented which showâ€¦ (More)

We discuss Levin-type sequence transformations {sn} â†’ {sn} that depend linearly on the sequence elements sn, and nonlinearly on an auxiliary sequence of remainder estimates {Ï‰n}. If the remainderâ€¦ (More)

The acceleration of slowly convergent Fourier series is discussed. For instance, such series arise in spectral methods with irregular grids as are required to resolve shock waves or other narrowâ€¦ (More)

Estimators Î n for the correlation energy can be computed as roots of effective characteristic polynomials of degree n. The coefficients of these polynomials are derived from the terms of theâ€¦ (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. Theâ€¦ (More)

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 Levinâ€¦ (More)

Recently, Sidi [Sidi, A. (1995): Acceleration of convergen c of (generalized) Fourier series by the d-transformation. Ann. Numer. Math. 2, 381â€“406] proposed a method for the convergence accelerati onâ€¦ (More)

Using sequence transformation and extrapolation algorithms for the prediction of further sequence elements from a finite number of known sequence elements is a topic of growing importance in appliedâ€¦ (More)