Brezinski / Redivo Zaglia Extrapolation Methods

Theory and Practice
1. Auflage 2013
ISBN: 978-0-08-050622-7
Verlag: Elsevier Science & Techn.
Format: PDF
Kopierschutz: 1 - PDF Watermark

E-Book, Englisch, Band Volume 2, 474 Seiten, Web PDF

Reihe: Studies in Computational Mathematics

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.

Autoren/Hrsg.

Brezinski, C.

Redivo Zaglia, M.

Inhaltsverzeichnis

1;Front Cover;1
2;Extrapolation Methods: Theory and Practice;4
3;Copyright Page;5
4;Table of Contents;8
5;Preface;6
6;Chapter 1. INTRODUCTION TO THE THEORY;12
6.1;1.1 First steps;12
6.2;1.2 What is an extrapolation method?;16
6.3;1.3 What is an extrapolation algorithm?;19
6.4;1.4 Quasi-linear sequence transformations;22
6.5;1.5 Sequence transformations as ratios of determinants;29
6.6;1.6 Triangular recursive schemes;32
6.7;1.7 Normal forms of the algorithms;37
6.8;1.8 Progressive forms of the algorithms;39
6.9;1.9 Particular rules of the algorithms;45
6.10;1.10 Accelerability and non-accelerability;50
6.11;1.11 Optimality;53
6.12;1.12 Asymptotic behaviour of sequences;58
7;Chapter 2. SCALAR EXTRAPOLATION ALGORITHMS;66
7.1;2.1 The E-algorithm;66
7.2;2.2 Richardson extrapolation process;83
7.3;2.3 The e-algorithm;89
7.4;2.4 The G-transformation;106
7.5;2.5 Rational extrapolation;112
7.6;2.6 Generalizations of the e-algorithm;119
7.7;2.7 Levin's transforms;124
7.8;2.8 Overholt's process;130
7.9;2.9 T-type algorithms;132
7.10;2.10 The iterated .2 process;139
7.11;2.11 Miscellaneous algorithms;142
8;Chapter 3. SPECIAL DEVICES;156
8.1;3.1 Error estimates and acceleration;156
8.2;3.2 Convergence tests and acceleration;162
8.3;3.3 Construction of asymptotic expansions;170
8.4;3.4 Construction of extrapolation processes;176
8.5;3.5 Extraction procedures;185
8.6;3.6 Automatic selection;189
8.7;3.7 Composite sequence transformations;196
8.8;3.8 Error control;204
8.9;3.9 Contractive sequence transformations;212
8.10;3.10 Least squares extrapolation;221
9;Chapter 4. VECTOR EXTRAPOLATION ALGORITHMS;224
9.1;4.1 The vector e-algorithm;227
9.2;4.2 The topological e-algorithm;231
9.3;4.3 The vector E-algorithm;239
9.4;4.4 The recursive projection algorithm;244
9.5;4.5 The H-algorithm;249
9.6;4.6 The Ford-Sidi algorithms;255
9.7;4.7 Miscellaneous algorithms;258
10;Chapter 5. CONTINUOUS PREDICTION ALGORITHMS;264
10.1;5.1 The Taylor expansion;265
10.2;5.2 Confluent Overholt's process;266
10.3;5.3 Confluent e-algorithms;267
10.4;5.4 Confluent .-algorithm;273
10.5;5.5 Confluent G-transform;276
10.6;5.6 Confluent E-algorithm;277
10.7;5.7 T-type confluent algorithms;278
11;Chapter 6. APPLICATIONS;280
11.1;6.1 Sequences and series;281
11.2;6.2 Systems of equations;313
11.3;6.3 Eigenelements;343
11.4;6.4 Integral and differential equations;349
11.5;6.5 Interpolation and approximation;365
11.6;6.6 Statistics;368
11.7;6.7 Integration and differentiation;376
11.8;6.8 Prediction;400
12;Chapter 7. SOFTWARE;408
12.1;7.1 Programming the algorithms;408
12.2;7.2 Computer arithmetic;411
12.3;7.3 Programs;414
13;Bibliography;424
14;Index;466