LEADER 04198nam 22006495 450 001 9910300134203321 005 20200629133841.0 010 $a3-319-94911-X 024 7 $a10.1007/978-3-319-94911-6 035 $a(CKB)4100000006675044 035 $a(DE-He213)978-3-319-94911-6 035 $a(MiAaPQ)EBC6242225 035 $a(PPN)230538142 035 $a(EXLCZ)994100000006675044 100 $a20180920d2018 u| 0 101 0 $aeng 135 $aurnn|008mamaa 181 $ctxt$2rdacontent 182 $cc$2rdamedia 183 $acr$2rdacarrier 200 10$aSplines and PDEs: From Approximation Theory to Numerical Linear Algebra $eCetraro, Italy 2017 /$fby Angela Kunoth, Tom Lyche, Giancarlo Sangalli, Stefano Serra-Capizzano ; edited by Tom Lyche, Carla Manni, Hendrik Speleers 205 $a1st ed. 2018. 210 1$aCham :$cSpringer International Publishing :$cImprint: Springer,$d2018. 215 $a1 online resource (IX, 318 p. 62 illus., 51 illus. in color.) 225 1 $aC.I.M.E. Foundation Subseries ;$v2219 311 $a3-319-94910-1 320 $aIncludes bibliographical references. 327 $aFoundations 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. 330 $aThis book takes readers on a multi-perspective tour through state-of-the-art mathematical developments related to the numerical treatment of PDEs based on splines, and in particular isogeometric methods. A wide variety of research topics are covered, ranging from approximation theory to structured numerical linear algebra. More precisely, the book provides (i) a self-contained introduction to B-splines, with special focus on approximation and hierarchical refinement, (ii) a broad survey of numerical schemes for control problems based on B-splines and B-spline-type wavelets, (iii) an exhaustive description of methods for computing and analyzing the spectral distribution of discretization matrices, and (iv) a detailed overview of the mathematical and implementational aspects of isogeometric analysis. The text is the outcome of a C.I.M.E. summer school held in Cetraro (Italy), July 2017, featuring four prominent lecturers with different theoretical and application perspectives. The book may serve both as a reference and an entry point into further research. 410 0$aC.I.M.E. Foundation Subseries ;$v2219 606 $aNumerical analysis 606 $aApproximation theory 606 $aPartial differential equations 606 $aNumerical Analysis$3https://scigraph.springernature.com/ontologies/product-market-codes/M14050 606 $aApproximations and Expansions$3https://scigraph.springernature.com/ontologies/product-market-codes/M12023 606 $aPartial Differential Equations$3https://scigraph.springernature.com/ontologies/product-market-codes/M12155 615 0$aNumerical analysis. 615 0$aApproximation theory. 615 0$aPartial differential equations. 615 14$aNumerical Analysis. 615 24$aApproximations and Expansions. 615 24$aPartial Differential Equations. 676 $a511.42 700 $aKunoth$b Angela$4aut$4http://id.loc.gov/vocabulary/relators/aut$0785951 702 $aLyche$b Tom$4aut$4http://id.loc.gov/vocabulary/relators/aut 702 $aSangalli$b Giancarlo$4aut$4http://id.loc.gov/vocabulary/relators/aut 702 $aSerra-Capizzano$b Stefano$4aut$4http://id.loc.gov/vocabulary/relators/aut 702 $aLyche$b Tom$4edt$4http://id.loc.gov/vocabulary/relators/edt 702 $aManni$b Carla$4edt$4http://id.loc.gov/vocabulary/relators/edt 702 $aSpeleers$b Hendrik$4edt$4http://id.loc.gov/vocabulary/relators/edt 801 0$bMiAaPQ 801 1$bMiAaPQ 801 2$bMiAaPQ 906 $aBOOK 912 $a9910300134203321 996 $aSplines and PDEs: From Approximation Theory to Numerical Linear Algebra$91923097 997 $aUNINA