Extrapolation Methods: Volume 2
Theory and Practice
Published on 21. November 1991
Book
Hardback
474 pages
978-0-444-88814-3 (ISBN)
Description
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.
Reviews / Votes
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.Newsletter on Computational and Applied Mathematics
Alan M. Cohen
The authors are to be commended... a valuable bibliography of almost 500 references...
Mathematical Reviews
More details
Series
Language
English
Place of publication
United States
Publishing group
Elsevier Science & Technology
Target group
Professional and scholarly
Weight
1160 gr
ISBN-13
978-0-444-88814-3 (9780444888143)
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Additional editions
E-Book
10/2013
Elsevier
€54.95
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Persons
Content
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.