Splines and PDEs: From Approximation Theory to Numerical Linear Algebra Cetraro, Italy 2017 /

• Κύριοι συγγραφείς: Kunoth, Angela (Συγγραφέας, http://id.loc.gov/vocabulary/relators/aut), Lyche, Tom (http://id.loc.gov/vocabulary/relators/aut, Επιμελητής έκδοσης, http://id.loc.gov/vocabulary/relators/edt), Sangalli, Giancarlo (http://id.loc.gov/vocabulary/relators/aut), Serra-Capizzano, Stefano (http://id.loc.gov/vocabulary/relators/aut)
• Συγγραφή απο Οργανισμό/Αρχή: SpringerLink (Online service)
• Άλλοι συγγραφείς: Manni, Carla (Επιμελητής έκδοσης, http://id.loc.gov/vocabulary/relators/edt), Speleers, Hendrik (Επιμελητής έκδοσης, http://id.loc.gov/vocabulary/relators/edt)
• Μορφή: Ηλεκτρονική πηγή Ηλ. βιβλίο
• Γλώσσα: English
• Έκδοση: Cham : Springer International Publishing : Imprint: Springer, 2018.
• Έκδοση: 1st ed. 2018.
• Σειρά: C.I.M.E. Foundation Subseries ; 2219
• Θέματα: Numerical analysis.; Approximation theory.; Partial differential equations.; Numerical Analysis.; Approximations and Expansions.; Partial Differential Equations.

 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. 

 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.