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Metric algebraic geometry

紀錄類型:	書目-電子資源 : Monograph/item
正題名/作者:	Metric algebraic geometry/ by Paul Breiding, Kathlen Kohn, Bernd Sturmfels.
作者:	Breiding, Paul.
其他作者:	Kohn, Kathlen.
出版者:	Cham :Springer Nature Switzerland : : 2024.,
面頁冊數:	xiv, 215 p. :ill., digital ;24 cm.
內容註:	Preface -- Historical Snapshot -- Critical Equations -- Computations -- Polar Degrees -- Wasserstein Distance -- Curvature -- Reach and Offset -- Voronoi Cells -- Condition Numbers -- Machine Learning -- Maximum Likelihood -- Tensors -- Computer Vision -- Volumes of Semialgebraic Sets -- Sampling -- References.
Contained By:	Springer Nature eBook
標題:	Geometry, Algebraic - Congresses. -
電子資源:	https://doi.org/10.1007/978-3-031-51462-3
ISBN:	9783031514623

Metric algebraic geometry
Breiding, Paul.

Metric algebraic geometry[electronic resource] /by Paul Breiding, Kathlen Kohn, Bernd Sturmfels. - Cham :Springer Nature Switzerland :2024. - xiv, 215 p. :ill., digital ;24 cm. - Oberwolfach seminars,v. 532296-5041 ;. - Oberwolfach seminars ;v. 53..

Preface -- Historical Snapshot -- Critical Equations -- Computations -- Polar Degrees -- Wasserstein Distance -- Curvature -- Reach and Offset -- Voronoi Cells -- Condition Numbers -- Machine Learning -- Maximum Likelihood -- Tensors -- Computer Vision -- Volumes of Semialgebraic Sets -- Sampling -- References.

Open access.

Metric algebraic geometry combines concepts from algebraic geometry and differential geometry. Building on classical foundations, it offers practical tools for the 21st century. Many applied problems center around metric questions, such as optimization with respect to distances. After a short dive into 19th-century geometry of plane curves, we turn to problems expressed by polynomial equations over the real numbers. The solution sets are real algebraic varieties. Many of our metric problems arise in data science, optimization and statistics. These include minimizing Wasserstein distances in machine learning, maximum likelihood estimation, computing curvature, or minimizing the Euclidean distance to a variety. This book addresses a wide audience of researchers and students and can be used for a one-semester course at the graduate level. The key prerequisite is a solid foundation in undergraduate mathematics, especially in algebra and geometry. This is an open access book.

ISBN: 9783031514623

Standard No.: 10.1007/978-3-031-51462-3doiSubjects--Topical Terms:

540562
Geometry, Algebraic
--Congresses.

LC Class. No.: QA564

Dewey Class. No.: 516.35

Metric algebraic geometry
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506 $a Open access.
520 $a Metric algebraic geometry combines concepts from algebraic geometry and differential geometry. Building on classical foundations, it offers practical tools for the 21st century. Many applied problems center around metric questions, such as optimization with respect to distances. After a short dive into 19th-century geometry of plane curves, we turn to problems expressed by polynomial equations over the real numbers. The solution sets are real algebraic varieties. Many of our metric problems arise in data science, optimization and statistics. These include minimizing Wasserstein distances in machine learning, maximum likelihood estimation, computing curvature, or minimizing the Euclidean distance to a variety. This book addresses a wide audience of researchers and students and can be used for a one-semester course at the graduate level. The key prerequisite is a solid foundation in undergraduate mathematics, especially in algebra and geometry. This is an open access book.
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