LEADER 03679nam 2200577 450 001 996466623303316 005 20220907162350.0 010 $a3-540-47300-9 024 7 $a10.1007/BFb0088788 035 $a(CKB)1000000000437116 035 $a(DE-He213)978-3-540-47300-8 035 $a(MiAaPQ)EBC5592329 035 $a(Au-PeEL)EBL5592329 035 $a(OCoLC)1066178687 035 $a(MiAaPQ)EBC6842106 035 $a(Au-PeEL)EBL6842106 035 $a(PPN)155210734 035 $a(EXLCZ)991000000000437116 100 $a20220907d1992 uy 0 101 0 $aeng 135 $aurnn#008mamaa 181 $ctxt$2rdacontent 182 $cc$2rdamedia 183 $acr$2rdacarrier 200 10$aMultivariate Birkhoff interpolation /$fRudolph A. Lorentz 205 $a1st ed. 1992. 210 1$aBerlin :$cSpringer-Verlag,$d[1992] 210 4$dİ1992 215 $a1 online resource (X, 198 p.) 225 1 $aLecture notes in mathematics (Springer-Verlag) ;$v1516 311 $a0-387-55870-5 311 $a3-540-55870-5 327 $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. 330 $aThe subject of this book is Lagrange, Hermite and Birkhoff (lacunary Hermite) interpolation by multivariate algebraic polynomials. It unifies and extends a new algorithmic approach to this subject which was introduced and developed by G.G. Lorentz and the author. One particularly interesting feature of this algorithmic approach is that it obviates the necessity of finding a formula for the Vandermonde determinant of a multivariate interpolation in order to determine its regularity (which formulas are practically unknown anyways) by determining the regularity through simple geometric manipulations in the Euclidean space. Although interpolation is a classical problem, it is surprising how little is known about its basic properties in the multivariate case. The book therefore starts by exploring its fundamental properties and its limitations. The main part of the book is devoted to a complete and detailed elaboration of the new technique. A chapter with an extensive selection of finite elements follows as well as a chapter with formulas for Vandermonde determinants. Finally, the technique is applied to non-standard interpolations. The book is principally oriented to specialists in the field. However, since all the proofs are presented in full detail and since examples are profuse, a wider audience with a basic knowledge of analysis and linear algebra will draw profit from it. Indeed, the fundamental nature of multivariate nature of multivariate interpolation is reflected by the fact that readers coming from the disparate fields of algebraic geometry (singularities of surfaces), of finite elements and of CAGD will also all find useful information here. 410 0$aLecture notes in mathematics (Springer-Verlag) ;$v1516. 606 $aInterpolation 606 $aSpline theory 615 0$aInterpolation. 615 0$aSpline theory. 676 $a511.42 686 $a41A05$2msc 686 $a41A63$2msc 686 $a65D05$2msc 700 $aLorentz$b Rudolph A.$059555 801 0$bMiAaPQ 801 1$bMiAaPQ 801 2$bMiAaPQ 906 $aBOOK 912 $a996466623303316 996 $aMultivariate Birkhoff interpolation$978669 997 $aUNISA