03580nam a22005295i 4500001001800000003000900018005001700027007001500044008004100059020001800100024003500118050001400153072001700167072002300184072001600207245016100223250001800384264007200402300006700474336002600541337002600567338003600593347002400629490004400653505090200697520077201599650002602371650002402397650001302421650001402434650001402448650003502462650002402497650001302521650001402534650001402548700007802562700007502640700007702715710003402792773002602826776003602852776003602888776003602924830004402960856004603004978-981-97-6508-9DE-He21320251030114635.0cr nn 008mamaa241223s2024    si |    s    |||| 0|eng d  a97898197650897 a10.1007/978-981-97-6508-92doi 4aQA221-224 7aPBKJ2bicssc 7aMAT0340002bisacsh 7aPBKJ2thema10aApproximation Theory and Numerical Analysis Meet Algebra, Geometry, Topologyh[electronic resource] /cedited by Martina Lanini, Carla Manni, Henry Schenck.  a1st ed. 2024. 1aSingapore :bSpringer Nature Singapore :bImprint: Springer,c2024.  aVIII, 330 p. 121 illus., 74 illus. in color.bonline resource.  atextbtxt2rdacontent  acomputerbc2rdamedia  aonline resourcebcr2rdacarrier  atext filebPDF2rda1 aSpringer INdAM Series,x2281-5198 ;v600 aIntroduction -- Bernstein Bézier form and its role in studying multivariate splines -- The algebra of splines group actions and homology -- A study on approximation by quartic splines defined on refined triangulations -- Construction of 2D explicit cubic -- Overlap Splines and Meshless Finite Difference -- A characterization of linear independence of THB splines in R n -- Restriction and Extension for planar splines on triangulations -- Supersmoothness of multivariate splines -- Using Geometric Symmetries to Achieve Super Smoothness for Cubic Powell-Sabin Splines -- Finite element diagram chasing -- On tensor product bases of PHT splinespaces -- Momentum graphs, Chinese remainder theorem and the surjectivity of the restriction map -- A Parsimonious Approach to $C^2$ Cubic Splines on Arbitrary Triangulations -- Alcove Walks and GKM Theory for Affine Flags -- Open problems in splines.  aThe book, based on the INdAM Workshop "Approximation Theory and Numerical Analysis Meet Algebra, Geometry, Topology" provides a bridge between different communities of mathematicians who utilize splines in their work. Splines are mathematical objects which allow researchers in geometric modeling and approximation theory to tackle a wide variety of questions. Splines are interesting for both applied mathematicians, and also for those working in purely theoretical mathematical settings. This book contains contributions by researchers from different mathematical communities: on the applied side, those working in numerical analysis and approximation theory, and on the theoretical side, those working in GKM theory, equivariant cohomology and homological algebra. 0aApproximation theory. 0aNumerical analysis. 0aAlgebra. 0aGeometry. 0aTopology.14aApproximations and Expansions.24aNumerical Analysis.24aAlgebra.24aGeometry.24aTopology.1 aLanini, Martina.eeditor.4edt4http://id.loc.gov/vocabulary/relators/edt1 aManni, Carla.eeditor.4edt4http://id.loc.gov/vocabulary/relators/edt1 aSchenck, Henry.eeditor.4edt4http://id.loc.gov/vocabulary/relators/edt2 aSpringerLink (Online service)0 tSpringer Nature eBook08iPrinted edition:z978981976507208iPrinted edition:z978981976509608iPrinted edition:z9789819765102 0aSpringer INdAM Series,x2281-5198 ;v6040uhttps://doi.org/10.1007/978-981-97-6508-9