Solving Problems with Projections: From Phase Retrieval to Packing - Tapa dura

Elser, Veit

 
9781009475525: Solving Problems with Projections: From Phase Retrieval to Packing
Tapa dura
ISBN 10: 1009475525 ISBN 13: 9781009475525
Editorial: Cambridge University Press, 2025

Sinopsis

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.

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Acerca del autor

Veit Elser, a Professor of Physics at Cornell University, is an expert in phase retrieval. His first major professional achievement was recognising that the atomic positions in quasicrystals could be understood as projections of points from a six-dimensional space into three dimensions. Projections continued to play a key role in his career, notably in 2001, when he discovered that the leading algorithm for solving the phase-retrieval problem was based on a pair of competing projections. Elser's work in physics was recognized by the William L. McMillan Prize.

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Editorial
Cambridge University Press
Año de publicación
2025
Idioma
Inglés
ISBN 10 
1009475525
ISBN 13 
9781009475525
Encuadernación
Tapa dura
Número de páginas
388
Contacto del fabricante
Cambridge University Press
https://www.cambridge.org/

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