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.
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Editorial Reviews
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"Destined to be a classic of modern computational science ... a gourmet feast in ten courses." -- from the foreword by David H. Bailey, Lawrence Berkeley National Laboratory
Book Description
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.
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Most Helpful Customer Reviews
3 of 3 people found the following review helpful:
5.0 out of 5 stars
A goldmine of clever numeric techniques,
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This review is from: The SIAM 100-Digit Challenge: A Study in High-Accuracy Numerical Computing (Paperback)
This book is not for beginners. But for anyone interested in numerical
analysis techniques, and with at least a full course or comparable experience, it is an absolute goldmine of clever ideas with working code, mostly in MATLAB or Mathematica. Each of 10 problems is solved by several different techniques, usually to multiple numbers of significant digits, with either proofs or ways to estimate the number of correct digits or how much work is required to get the number of correct digits one is interested in. Nicely written with an excellent bibliography and introductory summary in an Appendix. A few errors here and there in the equations, maybe a deliberate test of whether the reader is paying attention. Highly recommended to the indicated audience.
1 of 1 people found the following review helpful:
4.0 out of 5 stars
good book with details a few colorful pictures though a little expensive,
This review is from: The SIAM 100-Digit Challenge: A Study in High-Accuracy Numerical Computing (Paperback)
This is a good book containing a lot about high accuracy computation. Ten problems are discussed with details related to many areas of mathematics. A lot of codes of many mathematics software are shown with a helpful appendix. A web page of this book is also a highlight. You can even practice with it exhaustingly and enjoyably.
4 of 7 people found the following review helpful:
5.0 out of 5 stars
Clever techniques in a concrete context,
By
This review is from: The SIAM 100-Digit Challenge: A Study in High-Accuracy Numerical Computing (Paperback)
The book is ogranized by problem, not technique, and so the motivation is apparent before the theory is introduced. Some of the solutions are so clever they seem almost magical.
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Inside This Book
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First Sentence:
The 100-Digit Challenge began in 2001 when Lloyd N. Trefethen of Oxford University approched SIAM with the idea of publishing 10 challenging problems in numerical computing. Read the first page Key Phrases - Statistically Improbable Phrases (SIPs): (learn more)
sinh transformation, theta algorithm, rho algorithm, epsilon algorithm, relative discretization error, web page for this book, trapezoidal sums, terminal accuracy, singular moduli, correct digits, linear extrapolation methods, convergence acceleration, extrapolation table, using interval arithmetic, working precision, richardson extrapolation, partial difference equation, power iteration, machine arithmetic, interval algorithm, starting site, linear solver, secant method, posteriori error estimates, minimal eigenvalue Key Phrases - Capitalized Phrases (CAPs): (learn more)
Monte Carlo, Harder Problems, Solving It Analytically, Maple Session, Solving It Numerically, Wolfram Research, John Boersma New!
Books on Related Topics | Concordance | Text Stats Browse Sample Pages:
Front Cover | Table of Contents | First Pages | Index | Back Cover | Surprise Me!
The 100-Digit Challenge began in 2001 when Lloyd N. Trefethen of Oxford University approched SIAM with the idea of publishing 10 challenging problems in numerical computing. Read the first page Key Phrases - Statistically Improbable Phrases (SIPs): (learn more)
sinh transformation, theta algorithm, rho algorithm, epsilon algorithm, relative discretization error, web page for this book, trapezoidal sums, terminal accuracy, singular moduli, correct digits, linear extrapolation methods, convergence acceleration, extrapolation table, using interval arithmetic, working precision, richardson extrapolation, partial difference equation, power iteration, machine arithmetic, interval algorithm, starting site, linear solver, secant method, posteriori error estimates, minimal eigenvalue Key Phrases - Capitalized Phrases (CAPs): (learn more)
Monte Carlo, Harder Problems, Solving It Analytically, Maple Session, Solving It Numerically, Wolfram Research, John Boersma New!
Books on Related Topics | Concordance | Text Stats Browse Sample Pages:
Front Cover | Table of Contents | First Pages | Index | Back Cover | Surprise Me!
Citations (learn more)
This book cites 10
books:
See all 10 books this book cites
- Applied Mathematics by Cohen in Back Matter
- Waldo Emerson by Gay Wilson Allen on page 33
- British Columbia (Bugaboo mountain cover) by Douglas Leighton on page 2
- Numerical Recipes: The Art of Scientific Computing by William H. Press on page 77
- Numerical Analysis: Demonstrations on the HP-33E by Peter Henrici in Back Matter
See all 10 books this book cites
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