Extrapolation Methods - 1st Edition - ISBN: 9780444888143, 9780080506227

Extrapolation Methods, Volume 2

1st Edition

Theory and Practice

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Authors: C. Brezinski M. Redivo Zaglia
eBook ISBN: 9780080506227
Imprint: North Holland
Published Date: 21st November 1991
Page Count: 474
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Table of Contents

Introduction to the Theory. First Steps. What is an Extrapolation Method? What is an Extrapolation Algorithm? Quasi-linear Sequence Transformations. Sequence Transformations as Ratios of Determinants. Triangular Recursive Schemes. Normal Forms of the Algorithms. Progressive Forms of the Algorithms. Particular Rules of the Algorithms. Accelerability and Non-accelerability. Optimality. Asymptotic Behaviour of Sequences. Scalar Extrapolation Algorithms. The E-algorithm. Richardson Extrapolation Process. The &egr;-algorithm. The G-transformation. Rational Extrapolation. Generalizations of the &egr;-algorithm. Levin's Transformations. Overholt's Process. &THgr;-type Algorithms. The Iterated &Dgr;2 Process. Miscellaneous Algorithms. Special Devices. Error Estimates and Acceleration. Convergence Tests and Acceleration. Construction of Asymptotic Expansions. Construction of Extrapolation Processes. Extraction Procedures. Automatic Selection. Composite Sequence Transformations. Error Control. Contractive Sequence Transformations. Least Squares Extrapolation. Vector Extrapolation Algorithms. The Vector &egr;-algorithm. The Topological &egr;-algorithm. The Vector E-algorithm. The Recursive Projection Algorithm. The H-algorithm. The Ford-Sidi Algorithms. Miscellaneous Algorithms. Continuous Prediction Algorithms. The Taylor Expansion. Confluent Overholt's process. Confluent &egr;-algorithms. Confluent &rgr;-algorithm. Confluent G-transform. Confluent E-algorithm. &THgr;-type Confluent Algorithms. Applications. Sequences and Series: Simple Sequences, Double Sequences, Chebyshev and Fourier Series, Continued Fractions, Vector Sequences. Systems of Equations: Linear Systems, Projection Methods, Regularization and Penalty Techniques, Nonlinear Equations, Continuation Methods. Eigenelements: Eigenvalues and eigenvectors, Derivatives of Eigensystems. Integral and Differential Equations: Implicit Runge-Kutta Methods, Boundary Value Problems, Nonlinear Methods, Laplace Transform Inversion, Partial Differential Equations. Interpolation and Approximation. Statistics: The Jackknife, ARMA Models, Monte-Carlo Methods. Integration and Differentiation: Acceleration of Quadrature Formulae, Nonlinear Quadrature Formulae, Cauchy's Principal Values, Infinite Integrals, Multiple Integrals, Numerical Differentiation. Prediction. Software. Programming the Algorithms. Computer Arithmetic. Programs. Bibliography. Index.


This volume is a self-contained, exhaustive exposition of the extrapolation methods theory, and of the various algorithms and procedures for accelerating the convergence of scalar and vector sequences. Many subroutines (written in FORTRAN 77) with instructions for their use are provided on a floppy disk in order to demonstrate to those working with sequences the advantages of the use of extrapolation methods. Many numerical examples showing the effectiveness of the procedures and a consequent chapter on applications are also provided – including some never before published results and applications. Although intended for researchers in the field, and for those using extrapolation methods for solving particular problems, this volume also provides a valuable resource for graduate courses on the subject.


No. of pages:
© North Holland 1991
21st November 1991
North Holland
eBook ISBN:


@qu:This book is like an encyclopedia for extrapolation methods. It is a valuable source for researchers and students interested in the theory as well as in the practical application. It will certainly promote the use of extrapolation methods and that is a blessing for the computational and applied mathematics community. @source:Newsletter on Computational and Applied Mathematics @from:Alan M. Cohen @qu:The authors are to be commended... a valuable bibliography of almost 500 references... @source:Mathematical Reviews

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About the Authors

C. Brezinski Author

Affiliations and Expertise

Université des Sciences et Techniques de Lille Flandres-Trtois, Villeneuve d'Ascq, France

M. Redivo Zaglia Author

Affiliations and Expertise

Universitá degli Studi di Padova, Padova, Italy