Lp-error Bounds for Multivariate Polynomial Interpolation Schemes PDF Download
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Author: Shayne Waldron
Publisher:
ISBN:
Category :
Languages : en
Pages : 154
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Book Description
Author: Shayne Waldron
Publisher:
ISBN:
Category :
Languages : en
Pages : 154
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Book Description
Author: Rudolph A. Lorentz
Publisher: Springer
ISBN: 3540473009
Category : Mathematics
Languages : en
Pages : 200
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Book Description
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.
Author: Tom Lyche
Publisher:
ISBN:
Category : Computers
Languages : en
Pages : 584
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Book Description
"This volume contains a carefully refereed and edited selection of papers that were presented at the Oslo Conference on Mathematical Methods for Curves and Surfaces in July 2000. It contains several invited surveys written by leading experts in the field, along with contributed research papers on the most current developments in the theory and application of curves and surfaces."--Page 4 de la couverture.
Author: Dominik Stahl
Publisher:
ISBN:
Category :
Languages : en
Pages : 0
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Book Description
Author: N. K. Govil
Publisher: CRC Press
ISBN: 1420011383
Category : Mathematics
Languages : en
Pages : 476
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Book Description
Dedicated to the well-respected research mathematician Ambikeshwar Sharma, Frontiers in Interpolation and Approximation explores approximation theory, interpolation theory, and classical analysis. Written by authoritative international mathematicians, this book presents many important results in classical analysis, wavelets, and interpolation theory. Some topics covered are Markov inequalities for multivariate polynomials, analogues of Chebyshev and Bernstein inequalities for multivariate polynomials, various measures of the smoothness of functions, and the equivalence of Hausdorff continuity and pointwise Hausdorff-Lipschitz continuity of a restricted center multifunction. The book also provides basic facts about interpolation, discussing classes of entire functions such as algebraic polynomials, trigonometric polynomials, and nonperiodic transcendental entire functions. Containing both original research and comprehensive surveys, this book provides researchers and graduate students with important results of interpolation and approximation.
Author: David D. Watkins
Publisher:
ISBN:
Category : Interpolation
Languages : en
Pages : 48
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Book Description
Author: University of Wisconsin--Madison. Center for the Mathematical Sciences
Publisher:
ISBN:
Category : Mathematics
Languages : en
Pages : 646
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Book Description
Author: Patricia Jia Yiing Wong
Publisher:
ISBN:
Category : Hermite polynomials
Languages : en
Pages : 272
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Book Description
Author:
Publisher:
ISBN:
Category : Dissertations, Academic
Languages : en
Pages : 780
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Book Description
Author: D. Braess
Publisher: Birkhäuser
ISBN: 3034886195
Category : Science
Languages : en
Pages : 365
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Book Description
This book is the official proceedings of a conference on Numerical Methods in Approximation Theory which was held at the Mathematisches Forschungs institut in Oberwolfach during the week of November 24~30, 1991. It contains refereed and edited papers by 20 of the 49 participants. The book is dedicated to the memory of Prof. Lothar Collatz who main tained a long and active interest in numerical approximation. It is the ninth in a series of volumes published by Birkhiiuser resulting from conferences on the subject held at Oberwolfach, and co-organized by Prof. Collatz. We now briefly describe the contents of the book. The paper of BASZEN SKI, DELVOS and JESTER deals with blending using sine double series expan sions of functions defined on the unit square. In addition to giving explicit error estimates for partial sums and for interpolating sine polynomials, they also show that Boolean sums yield almost the same asymptotic error estimates as the conventional tensor-product approach, but with a reduced number of terms. The paper of BEATSON and LIGHT discusses approximation by quasi interpolants which are sums of scaled translates of a one-parameter family of functions. They do not require reproduction of low degree polynomials, but nevertheless are able to give error bounds and analyze quasi-interpolation based on Gaussians and exponentials. BINEV and JETTER deal with multivariate interpolation using shifts of a single basis function. They treat both gridded data and scattered data. As examples, they consider box splines and certain radial basis functions.
