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The SIAM 100-Digit Challenges : A Study in High-Accuracy Numerical Computing by
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eBay-Artikelnr.:146970721217
Artikelmerkmale
- Artikelzustand
- ISBN
- 9780898715613
Über dieses Produkt
Product Identifiers
Publisher
Society for Industrial AND Applied Mathematics
ISBN-10
089871561X
ISBN-13
9780898715613
eBay Product ID (ePID)
4038753611
Product Key Features
Number of Pages
318 Pages
Language
English
Publication Name
Siam 100-Digit Challenges : a Study in High-Accuracy Numerical Computing
Subject
Numerical Analysis, Mathematical Analysis
Publication Year
2004
Type
Textbook
Subject Area
Mathematics
Format
Trade Paperback
Dimensions
Item Height
0.8 in
Item Weight
20 Oz
Item Length
9 in
Item Width
6 in
Additional Product Features
Intended Audience
Scholarly & Professional
LCCN
2004-049139
TitleLeading
The
Dewey Edition
22
Illustrated
Yes
Dewey Decimal
518
Table Of Content
Foreword Preface The Story Chapter 1: A Twisted Tail Chapter 2: Reliability amid Chaos Chapter 3: How Far Away Is Infinity? Chapter 4: Think Globally Act Locally Chapter 5: A Complex Optimization Chapter 6: Biasing for a Fair Return Chapter 7: Too Large to Be Easy Too Small to Be Hard Chapter 8: In the Moment of Heat Chapter 9: Gradus ad Parnassum Chapter 10: Hitting the Ends Appendix A: Convergence Acceleration Appendix B: Extreme Digit-Hunting Appendix C: Code Appendix D: More Problems References Index.
Synopsis
The authors, members of teams that solved all 10 problems, show in detail multiple approaches for solving each problem, ranging from elementary to sophisticated, from brute-force to schemes that can be scaled to provide thousands of digits of accuracy and that can solve even larger related problems. The authors touch on virtually every major technique of modern numerical analysis: matrix computation, iterative linear methods, limit extrapolation and convergence acceleration, numerical quadrature, contour integration, discretization of PDEs, global optimization, Monte Carlo and evolutionary algorithms, error control, interval and high-precision arithmetic, and many more. The SIAM 100-Digit Challenge: A Study in High-Accuracy Numerical Computing gives concrete examples of how to justify the validity of every single digit of a numerical answer. Methods range from carefully designed computer experiments to a posteriori error estimates and computer-assisted proofs based on interval arithmetic., This book takes readers on a thrilling tour of some of the most important and powerful areas of contemporary numerical mathematics. The tour is organized along the 10 problems of the SIAM 100-Digit Challenge, a contest posed by Nick Trefethen of Oxford University in the January/February 2002 issue of SIAM News. The complete story of the contest as well as a lively interview with Nick Trefethen are also included. The authors, members of teams that solved all 10 problems, show in detail multiple approaches for solving each problem, ranging from elementary to sophisticated, from brute-force to schemes that can be scaled to provide thousands of digits of accuracy and that can solve even larger related problems. The authors touch on virtually every major technique of modern numerical analysis: matrix computation, iterative linear methods, limit extrapolation and convergence acceleration, numerical quadrature, contour integration, discretization of PDEs, global optimization, Monte Carlo and evolutionary algorithms, error control, interval and high-precision arithmetic, and many more. The SIAM 100-Digit Challenge: A Study in High-Accuracy Numerical Computing gives concrete examples of how to justify the validity of every single digit of a numerical answer. Methods range from carefully designed computer experiments to a posteriori error estimates and computer-assisted proofs based on interval arithmetic. This book will aid readers in developing problem-solving skills for making judicious method selections. The chapters may be read independently. Appendices A and B include basic methods of convergence acceleration and details of computing the solutions to very high accuracy. Full code for all the methods, examples, tables, and figures is given (partly in Appendix C, completely on the accompanying web page. The code is written in a variety of languages, including Mathematica, MATLAB, Maple, C, Octave, and PARI/GP. Appendix D offers a sample of additional challenging problems for those who master some of the techniques discussed here., Takes readers on a thrilling tour of some of the most important and powerful areas of contemporary numerical mathematics. The tour is organised along the 10 problems of the SIAM 100-Digit Challenge, a contest posed by Nick Trefethen of Oxford University in the January/February 2002 issue of SIAM News. The complete story of the contest as well as an interview with Nick Trefethen are also included.
LC Classification Number
QA297 .S4782 2004
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