04198nam 22006495 450 991030013420332120200629133841.03-319-94911-X10.1007/978-3-319-94911-6(CKB)4100000006675044(DE-He213)978-3-319-94911-6(MiAaPQ)EBC6242225(PPN)230538142(EXLCZ)99410000000667504420180920d2018 u| 0engurnn|008mamaatxtrdacontentcrdamediacrrdacarrierSplines and PDEs: From Approximation Theory to Numerical Linear Algebra Cetraro, Italy 2017 /by Angela Kunoth, Tom Lyche, Giancarlo Sangalli, Stefano Serra-Capizzano ; edited by Tom Lyche, Carla Manni, Hendrik Speleers1st ed. 2018.Cham :Springer International Publishing :Imprint: Springer,2018.1 online resource (IX, 318 p. 62 illus., 51 illus. in color.) C.I.M.E. Foundation Subseries ;22193-319-94910-1 Includes bibliographical references.Foundations of Spline Theory: B-Splines, Spline Approximation, and Hierarchical Refinement -- Adaptive Multiscale Methods for the Numerical Treatment of Systems of PDEs -- Generalized Locally Toeplitz Sequences: A Spectral Analysis Tool for Discretized Differential Equations -- Isogeometric Analysis: Mathematical and Implementational Aspects, with Applications.This book takes readers on a multi-perspective tour through state-of-the-art mathematical developments related to the numerical treatment of PDEs based on splines, and in particular isogeometric methods. A wide variety of research topics are covered, ranging from approximation theory to structured numerical linear algebra. More precisely, the book provides (i) a self-contained introduction to B-splines, with special focus on approximation and hierarchical refinement, (ii) a broad survey of numerical schemes for control problems based on B-splines and B-spline-type wavelets, (iii) an exhaustive description of methods for computing and analyzing the spectral distribution of discretization matrices, and (iv) a detailed overview of the mathematical and implementational aspects of isogeometric analysis. The text is the outcome of a C.I.M.E. summer school held in Cetraro (Italy), July 2017, featuring four prominent lecturers with different theoretical and application perspectives. The book may serve both as a reference and an entry point into further research.C.I.M.E. Foundation Subseries ;2219Numerical analysisApproximation theoryPartial differential equationsNumerical Analysishttps://scigraph.springernature.com/ontologies/product-market-codes/M14050Approximations and Expansionshttps://scigraph.springernature.com/ontologies/product-market-codes/M12023Partial Differential Equationshttps://scigraph.springernature.com/ontologies/product-market-codes/M12155Numerical analysis.Approximation theory.Partial differential equations.Numerical Analysis.Approximations and Expansions.Partial Differential Equations.511.42Kunoth Angelaauthttp://id.loc.gov/vocabulary/relators/aut785951Lyche Tomauthttp://id.loc.gov/vocabulary/relators/autSangalli Giancarloauthttp://id.loc.gov/vocabulary/relators/autSerra-Capizzano Stefanoauthttp://id.loc.gov/vocabulary/relators/autLyche Tomedthttp://id.loc.gov/vocabulary/relators/edtManni Carlaedthttp://id.loc.gov/vocabulary/relators/edtSpeleers Hendrikedthttp://id.loc.gov/vocabulary/relators/edtMiAaPQMiAaPQMiAaPQBOOK9910300134203321Splines and PDEs: From Approximation Theory to Numerical Linear Algebra1923097UNINA