Topics in Advanced Scientific Computation

Topics in Advanced Scientific Computation is a sequel to Crandall's highly successful Projects in Scientific Computation (TELOS / Springer-Verlag 1994). It delves into specific and sometimes difficult, research-oriented algorithms as they arise in the attempted solutions of computationally hard problems.

Topics in Advanced Scientific Computation is a tour of modern algorithms on the computational scene. Techniques and applications span the fields of engineering, mathematics, and computer science. The reader is rewarded with state-of-the-art algorithms including several striking new achievements.

The topics include: several numerical algorithms, evaluation of constants and functions, number-theoretic algorithms, transforms, nonlinear and complex systems, and data manipulation.

Most of the topics in the book have support code in the form of Mathematica notebooks and C source files. These files can be obtained from the TELOS Web site and run on a most computer platforms, including DOS/Windows, Macintosh, NEXTSTEP, and most Unix computers.

[Topics in Advanced Scientific Computatioin] is up-to-date with the latest algorithms and numerical results...it is a good source book...the author is enthusiastic and knowledgable about the subject matter...the material is fascinating!

---Richard Brent, Computer Sciences Laboratory
Australian National University


1996/320 pages/Hardcover
ISBN 0-387-94473-7

The source for the Mathematica and C programs can be obtained via the TELOS Web site. Mathematica 2.0 or higher is recommended to fully the notebooks.

MathReader is a freely available program that will allow you to read (and print) any Mathematica notebook on most computer platforms.

Preface

Chapter 1: Selected Numerical Algorithms

Variants of the Newton method, fast divide and mod algorithms, fast multiplication, matrix algebra, polynomial arithmetic

Chapter 2: Evaluation of Constants and Functions

Celebrated constants, Riemann zeta function, multidimensional sums, examples of special function evaluation

Chapter 3: Number-Theoretical Algorithms

Primes, celebrated conjectures, factoring, Fermat numbers

Chapter 4: Transforms

FFT and related algorithms, Walsh-Hadamard transform, wavelets, convolution

Chapter 5: Nonlinear and Complex Systems

N-body problems nad chaos, nonlinear differential equations, fractal analysis, learning algorithms, an old and beautiful nonlinear system

Chapter 6: Data Manipulation

Signal synthesis, detection and modeling, general data compression, sound and image compression

Appendix

Listing of code for all programs in text

References

Index

To Order