Topics in Advanced Scientific Computation

ISBN-13: 9781461275077 / Angielski / Miękka / 2011 / 340 str.

Richard E. Crandall

Opis

The major differences between this book and richard's previous title published with TELOS in Jan. '94, are that a) in "Projects" theory was stated, then projects listed as exercises. In "Topics" there will be a set of problems. while the author will refer to some of the more useful algotithms in the "Prjects" text, most algorithms in the "Topics" vilume will be distincly new. Also, b) while "Prjects" in a course book (in context and design) with assigned Problems, "Topics" is inteded as a research reference with stated solutions. The author feels this is an extention of "Projects." "Topics" has a 40-page appendix and no diskette. Finally, the overall style and level of presentation are directed towars the research professional in "Topics," rather than a textbook approach.

Recenzje

"This book is a fascinating glimpse into the mathematical and algorithmic byways into which one may be led from areas as diverse as signal analysis and complexity theory." Scientific Computing World

Spis treści

1 Selected numerical algorithms.- Variants of the Newton method.- Fast divide and mod algorithms.- Fast multiplication.- Matrix algebra.- Polynomial arithmetic.- 2 Evaluation of constants & functions.- Celebrated constants.- Riemann zeta function.- Multidimensional sums.- Examples of special function evaluation.- 3 Number-theoretical algorithms.- Primes.- Bernoulli numbers.- Factoring.- Fermat numbers.- 4 Transforms.- FFT and related algorithms.- Walsh-Hadamard transform.- Wavelets.- Convolution.- 5 Nonlinear & complex systems.- N-body problems & chaos.- Nonlinear differential systems.- Fractal analysis.- Learning algorithms.- An old & beautiful nonlinear system.- 6 Data manipulation.- Signal synthesis, detection and modeling.- General data compression.- Sound and image compression.- References.