03977nam a22006135i 4500 978-981-97-6508-9 DE-He213 20251030114635.0 cr nn 008mamaa 241223s2024 si | s |||| 0|eng d 9789819765089 978-981-97-6508-9 10.1007/978-981-97-6508-9 doi QA221-224 PBKJ bicssc MAT034000 bisacsh PBKJ thema Approximation Theory and Numerical Analysis Meet Algebra, Geometry, Topology [electronic resource] / edited by Martina Lanini, Carla Manni, Henry Schenck. 1st ed. 2024. Singapore : Springer Nature Singapore : Imprint: Springer, 2024. VIII, 330 p. 121 illus., 74 illus. in color. online resource. text txt rdacontent computer c rdamedia online resource cr rdacarrier text file PDF rda Springer INdAM Series, 2281-5198 ; 60 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. Approximation theory. 74825 Numerical analysis. Algebra. 1501 Geometry. 68763 Topology. 72917 Approximations and Expansions. 74827 Numerical Analysis. Algebra. 1501 Geometry. 68763 Topology. 72917 Lanini, Martina. editor. edt http://id.loc.gov/vocabulary/relators/edt 89455 Manni, Carla. editor. edt http://id.loc.gov/vocabulary/relators/edt 89456 Schenck, Henry. editor. edt http://id.loc.gov/vocabulary/relators/edt 89457 SpringerLink (Online service) Springer Nature eBook Printed edition: 9789819765072 Printed edition: 9789819765096 Printed edition: 9789819765102 Springer INdAM Series, 2281-5198 ; 60 77740 https://doi.org/10.1007/978-981-97-6508-9 ZDB-2-SMA ZDB-2-SXMS 65977 65977