03851nam 22006855 450 991091869760332120241223115634.09789819765089(electronic bk.)978981976507210.1007/978-981-97-6508-9(MiAaPQ)EBC31856117(Au-PeEL)EBL31856117(CKB)37077732200041(DE-He213)978-981-97-6508-9(EXLCZ)993707773220004120241223d2024 u| 0engurcnu||||||||txtrdacontentcrdamediacrrdacarrierApproximation Theory and Numerical Analysis Meet Algebra, Geometry, Topology /edited by Martina Lanini, Carla Manni, Henry Schenck1st ed. 2024.Singapore :Springer Nature Singapore :Imprint: Springer,2024.1 online resource (333 pages)Springer INdAM Series,2281-5198 ;60Print version: Lanini, Martina Approximation Theory and Numerical Analysis Meet Algebra, Geometry, Topology Singapore : Springer,c2025 9789819765072 Introduction -- 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.The 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.Springer INdAM Series,2281-5198 ;60Approximation theoryNumerical analysisAlgebraGeometryTopologyApproximations and ExpansionsNumerical AnalysisAlgebraGeometryTopologyApproximation theory.Numerical analysis.Algebra.Geometry.Topology.Approximations and Expansions.Numerical Analysis.Algebra.Geometry.Topology.511.4Lanini Martina1781207Manni Carla1781208Schenck Henry812671MiAaPQMiAaPQMiAaPQ9910918697603321Approximation Theory and Numerical Analysis Meet Algebra, Geometry, Topology4305962UNINA