000 03811nam a22004815i 4500
001 978-3-540-47300-8
003 DE-He213
005 20190213151519.0
007 cr nn 008mamaa
008 121227s1992 gw | s |||| 0|eng d
020 _a9783540473008
_9978-3-540-47300-8
024 7 _a10.1007/BFb0088788
_2doi
050 4 _aQA331.5
072 7 _aPBKB
_2bicssc
072 7 _aMAT034000
_2bisacsh
072 7 _aPBKB
_2thema
082 0 4 _a515.8
_223
100 1 _aLorentz, Rudolph A.
_eauthor.
_4aut
_4http://id.loc.gov/vocabulary/relators/aut
245 1 0 _aMultivariate Birkhoff Interpolation
_h[electronic resource] /
_cby Rudolph A. Lorentz.
264 1 _aBerlin, Heidelberg :
_bSpringer Berlin Heidelberg :
_bImprint: Springer,
_c1992.
300 _aX, 198 p.
_bonline resource.
336 _atext
_btxt
_2rdacontent
337 _acomputer
_bc
_2rdamedia
338 _aonline resource
_bcr
_2rdacarrier
347 _atext file
_bPDF
_2rda
490 1 _aLecture Notes in Mathematics,
_x0075-8434 ;
_v1516
505 0 _aUnivariate interpolation -- Basic properties of Birkhoff interpolation -- Singular interpolation schemes -- Shifts and coalescences -- Decomposition theorems -- Reduction -- Examples -- Uniform Hermite interpolation of tensor-product type -- Uniform Hermite interpolation of type total degree -- Vandermonde determinants -- A theorem of Severi -- Kergin interpolation via Birkhoff interpolation.
520 _aThe subject of this book is Lagrange, Hermite and Birkhoff (lacunary Hermite) interpolation by multivariate algebraic polynomials. It unifies and extends a new algorithmic approach to this subject which was introduced and developed by G.G. Lorentz and the author. One particularly interesting feature of this algorithmic approach is that it obviates the necessity of finding a formula for the Vandermonde determinant of a multivariate interpolation in order to determine its regularity (which formulas are practically unknown anyways) by determining the regularity through simple geometric manipulations in the Euclidean space. Although interpolation is a classical problem, it is surprising how little is known about its basic properties in the multivariate case. The book therefore starts by exploring its fundamental properties and its limitations. The main part of the book is devoted to a complete and detailed elaboration of the new technique. A chapter with an extensive selection of finite elements follows as well as a chapter with formulas for Vandermonde determinants. Finally, the technique is applied to non-standard interpolations. The book is principally oriented to specialists in the field. However, since all the proofs are presented in full detail and since examples are profuse, a wider audience with a basic knowledge of analysis and linear algebra will draw profit from it. Indeed, the fundamental nature of multivariate nature of multivariate interpolation is reflected by the fact that readers coming from the disparate fields of algebraic geometry (singularities of surfaces), of finite elements and of CAGD will also all find useful information here.
650 0 _aMathematics.
650 0 _aNumerical analysis.
650 1 4 _aReal Functions.
_0http://scigraph.springernature.com/things/product-market-codes/M12171
650 2 4 _aNumerical Analysis.
_0http://scigraph.springernature.com/things/product-market-codes/M14050
710 2 _aSpringerLink (Online service)
773 0 _tSpringer eBooks
776 0 8 _iPrinted edition:
_z9783662170588
776 0 8 _iPrinted edition:
_z9783540558705
830 0 _aLecture Notes in Mathematics,
_x0075-8434 ;
_v1516
856 4 0 _uhttps://doi.org/10.1007/BFb0088788
912 _aZDB-2-SMA
912 _aZDB-2-LNM
912 _aZDB-2-BAE
999 _c10928
_d10928