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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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SOLVING PROBLEMS WITH PROJECTIONS
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Solving Problems with Projections: From Phase Retrieval to Packing
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Solving Problems with Projections: From Phase Retrieval to Packing
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Solving Problems with Projections
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Buch. Condizione: Neu. Druck auf Anfrage Neuware - Printed after ordering - 'This book presents a novel method for tackling complex problems by framing them in 'bipartisan' terms and realizing the two 'parts' with projections. Written in an engaging, accessible style, it is an invaluable resource for scientists, engineers and applied mathematicians working on reconstruction problems, such as phase-retrieval'--. Codice articolo 9781009475525
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Solving Problems with Projections: From Phase Retrieval to Packing
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Solving Problems with Projections: From Phase Retrieval to Packing
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Solving Problems with Projections: From Phase Retrieval to Packing
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Solving Problems with Projections: From Phase Retrieval to Packing
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Solving Problems with Projections (Hardcover)
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Cambridge University Press, Cambridge, 2025
ISBN 10: 1009475525
ISBN 13: 9781009475525
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Hardcover. Condizione: new. Hardcover. 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. This book presents a novel method for tackling complex problems by framing them in 'bipartisan' terms and realizing the two 'parts' with projections. Written in an engaging, accessible style, it is an invaluable resource for scientists, engineers and applied mathematicians working on reconstruction problems, such as phase-retrieval. Shipping may be from our UK warehouse or from our Australian or US warehouses, depending on stock availability. Codice articolo 9781009475525
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