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Lorentz R.A. — Multivariate Birkhoff Interpolation

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Название: Multivariate Birkhoff Interpolation

Автор: Lorentz R.A.

Аннотация:

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:

Рубрика: Математика/

Статус предметного указателя: Готов указатель с номерами страниц

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Год издания: 1992

Количество страниц: 212

Добавлена в каталог: 02.07.2008

Операции: Положить на полку | Скопировать ссылку для форума | Скопировать ID
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       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       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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