Topics in Advanced Scientific Computation

• 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.

"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