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Lorentz R.A. — Multivariate Birkhoff Interpolation
Lorentz R.A. — Multivariate Birkhoff Interpolation

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Название: Multivariate Birkhoff Interpolation

Автор: Lorentz R.A.


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.

Язык: en

Рубрика: Математика/

Статус предметного указателя: Готов указатель с номерами страниц

ed2k: ed2k stats

Год издания: 1992

Количество страниц: 212

Добавлена в каталог: 02.07.2008

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Предметный указатель
Abel matrix      15
Almost regular, multivariate      10
Almost regular, univariate      3
Birkhoff interpolation scheme, multivariate      8
Birkhoff interpolation scheme, univariate      3
Class of a shift      48
Coalescence      57
Coefficient of collision      59
Collision of nodal matrices      48
Globally $C_{k}$      29
Hermite interpolation of tensor-product type      22
Hermite interpolation of type total degree      21
Hermite interpolation, univariate      5
Hermitian, nodal matrix      61
Hermitian, subset of $\mathbf{N}_{0}^{d}$      61
Image of a shift      48
Incidence matrix, multivariate      8
Incidence matrix, univariate      3
Line of a nodal matrix      53 59
Maximal coalescence      57
Maximal shift      49
Minimal coalescence      57
Minimal shift      49
Multiple shift      48
Multiplicity of a singularity      103
Nodal matrix      59
Normal incidence matrix, multivariate      10
Normal incidence matrix, univariate      3
Order of a shift      48
Order regular      4
Polya condition, multivariate      15
Polya condition, univariate      5
Precoalescence      57
Pyramidal numbers      40
Regular at Z      10
Regular, multivariate      10
Regular, univariate      4
Shift      48
Signed number of shifts      36
Simple shift      48
Singular, multivariate      10
Singular, univariate      4
Singularity      103
Support of a nodal matrix      11
Tetrahedral numbers      40
Triangular numbers      36
Uniform Hermite interpolation of tensor-product type      23
Uniform Hermite interpolation of type total degree      22
Unique class of shifts      48
Unique shift      48
Upper set      15
Vandermonde determinant      9
Vandermonde matrix      9
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