03679nam 2200577 450 99646662330331620220907162350.03-540-47300-910.1007/BFb0088788(CKB)1000000000437116(DE-He213)978-3-540-47300-8(MiAaPQ)EBC5592329(Au-PeEL)EBL5592329(OCoLC)1066178687(MiAaPQ)EBC6842106(Au-PeEL)EBL6842106(PPN)155210734(EXLCZ)99100000000043711620220907d1992 uy 0engurnn#008mamaatxtrdacontentcrdamediacrrdacarrierMultivariate Birkhoff interpolation /Rudolph A. Lorentz1st ed. 1992.Berlin :Springer-Verlag,[1992]©19921 online resource (X, 198 p.)Lecture notes in mathematics (Springer-Verlag) ;15160-387-55870-5 3-540-55870-5 Univariate 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.The 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.Lecture notes in mathematics (Springer-Verlag) ;1516.InterpolationSpline theoryInterpolation.Spline theory.511.4241A05msc41A63msc65D05mscLorentz Rudolph A.59555MiAaPQMiAaPQMiAaPQBOOK996466623303316Multivariate Birkhoff interpolation78669UNISA01367nas 2200469- 450 99619941740331620220531213022.02046-0260(DE-599)ZDB2667677-1(OCoLC)824458092(CKB)3280000000000273(CONSER)--2016207052(EXLCZ)99328000000000027320130115a20129999 --- aengur|||||||||||txtrdacontentcrdamediacrrdacarrierPsyCh journal[Weinheim] :Wiley-VCH VerlagDanvers, MA :Wiley Publishing Asia Pty Ltd.1 online resourceRefereed/Peer-reviewed2046-0252 PsychologyResearchPeriodicalsPsychologieRecherchePériodiquesPsychologyResearchfast(OCoLC)fst01081506Periodicals.fastpsychologiepsychologyPsychology (General)Psychologie (algemeen)PsychologyResearchPsychologieRecherchePsychologyResearch.150Zhongguo ke xue yuan.Xin li yan jiu suo,JOURNAL996199417403316PsyCh journal2228029UNISA