Practical Extrapolation Methods by Avram Sidi

The g-transformation and its generalizationsĢ2. The Wynn ρ- and Brezinski θ-algorithmsĢ1. The Euler transformation, Aitken Δ2-process, and Lubkin W-transformationĢ0. Special topics in Richardson extrapolationġ5. Acceleration of convergence of Fourier and generalized Fourier series by the d-transformation: the complex series approach with APSġ4. Acceleration of convergence of power series by the d-transformation: rational d-approximantsġ3. Reduction of the d-transformation for oscillatory infinite-range integrals: the D-, D-, W-, and mW-transformationsġ2. Analytic study of GREP(1): quickly varying A(y) ∈ F(1)ġ0: Efficient use of GREP(1): applications to the D(1)-, d(1)- and d(m)-transformationsġ1. Analytic study of GREP (1): slowly varying A(y) ∈ F(1)ĩ. The d-transformation: a GREP for infinite series and sequencesĨ. The d-transformation: a GREP for infinite-range integralsĦ. GREP: further generalization of the Richardson extrapolation processĥ. First generalization of the Richardson extrapolation processĤ. Additional topics in Richardson extrapolationģ. The Richardson Extrapolation Process and Its Generalizations:Ģ. It differs from existing books by concentrateing on the most powerful nonlinear methods, presenting in-depth treatments of them, and showing which methods are most effective for different classes of practical nontrivial problems. The methods discussed are geared toward common problems in scientific and engineering disciplines. This state-of-the art reference for mathematicians, scientists and engineers is concerned with the coherent treatment, including derivation, analysis, and applications, of the most useful scalar extrapolation methods. These limits can be approximated economically and with high accuracy by applying suitable extrapolation (or convergence acceleration) methods to a small number of terms.

Thus, to approximate limits with reasonable accuracy, it is necessary to compute a large number of terms, and this is in general costly. Description Product filter button DescriptionĪn important problem that arises in many scientific and engineering applications is that of approximating limits of infinite sequences which in most instances converge very slowly.

Practical Extrapolation Methods by Avram Sidi