Topics in Advanced Scientific Computation - R.E. Crandall

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Résumé :
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.

Sommaire:
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.