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001 978-3-031-51462-3
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008 240227s2024 sz | s |||| 0|eng d
020 _a9783031514623
_9978-3-031-51462-3
024 7 _a10.1007/978-3-031-51462-3
_2doi
050 4 _aQA564-609
072 7 _aPBMW
_2bicssc
072 7 _aMAT012010
_2bisacsh
072 7 _aPBMW
_2thema
082 0 4 _a516.35
_223
100 1 _aBreiding, Paul.
_eauthor.
_4aut
_4http://id.loc.gov/vocabulary/relators/aut
245 1 0 _aMetric Algebraic Geometry
_h[electronic resource] /
_cby Paul Breiding, Kathlén Kohn, Bernd Sturmfels.
250 _a1st ed. 2024.
264 1 _aCham :
_bSpringer Nature Switzerland :
_bImprint: Birkhäuser,
_c2024.
300 _aXIV, 215 p.
_bonline resource.
336 _atext
_btxt
_2rdacontent
337 _acomputer
_bc
_2rdamedia
338 _aonline resource
_bcr
_2rdacarrier
347 _atext file
_bPDF
_2rda
490 1 _aOberwolfach Seminars,
_x2296-5041 ;
_v53
505 0 _aPreface -- 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.
506 0 _aOpen Access
520 _aMetric 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.
650 0 _aAlgebraic geometry.
650 0 _aGeometry, Differential.
650 0 _aArtificial intelligence
_xData processing.
650 0 _aNumerical analysis.
650 1 4 _aAlgebraic Geometry.
650 2 4 _aDifferential Geometry.
650 2 4 _aData Science.
650 2 4 _aNumerical Analysis.
700 1 _aKohn, Kathlén.
_eauthor.
_4aut
_4http://id.loc.gov/vocabulary/relators/aut
700 1 _aSturmfels, Bernd.
_eauthor.
_4aut
_4http://id.loc.gov/vocabulary/relators/aut
710 2 _aSpringerLink (Online service)
773 0 _tSpringer Nature eBook
776 0 8 _iPrinted edition:
_z9783031514616
776 0 8 _iPrinted edition:
_z9783031514630
830 0 _aOberwolfach Seminars,
_x2296-5041 ;
_v53
856 4 0 _uhttps://doi.org/10.1007/978-3-031-51462-3
912 _aZDB-2-SMA
912 _aZDB-2-SXMS
912 _aZDB-2-SOB
999 _c37782
_d37782