Solving Problems with Projections: From Phase Retrieval to Packing - Rilegato

Veit Elser

Rilegato

ISBN 10: 1009475525 ISBN 13: 9781009475525

Casa editrice: Cambridge University Press, 2025

Riassunto

It is a curious fact that even notoriously difficult computational problems can be expressed in the form of a high-dimensional Venn diagram, where solutions lie in the overlap of a pair of remarkably simple sets, A and B. The simplicity of these sets enables operations called projections that locate the nearest point of A, or B, starting anywhere within the high-dimensional space.  This book introduces a novel method for tackling complex problems that exploits projections and the two-set structure, offering an effective alternative to traditional, gradient-based approaches. Beginning with phase retrieval, where A and B address the properties of an image and its Fourier transform, it progresses to more diverse challenges, such as sphere packing, origami design, sudoku and tiling puzzles, data dimension reduction, and neural network training. The text presents a detailed description of this powerful and original approach and is essential reading for physicists and applied mathematicians.

Dettagli dell'edizione

• Editore: Cambridge University Press
• Data di pubblicazione: 2025
• Lingua: Inglese
• ISBN 10: 1009475525
• ISBN 13: 9781009475525
• Rilegatura: Copertina rigida
• Numero di pagine: 386
• Contatto del produttore: Cambridge University Press; https://www.cambridge.org/; ; Via Honduras,15; Pomezia; Italia; 71; Italia