Multivariate Birkhoff Interpolation

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Publisher : Springer
ISBN 13 : 3540473009
Total Pages : 200 pages
Book Rating : 4.5/5 (44 download)

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Book Synopsis Multivariate Birkhoff Interpolation by : Rudolph A. Lorentz

Download or read book Multivariate Birkhoff Interpolation written by Rudolph A. Lorentz and published by Springer. This book was released on 2006-11-15 with total page 200 pages. Available in PDF, EPUB and Kindle. Book excerpt: 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.

Birkhoff Interpolation Problem

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Publisher :
ISBN 13 :
Total Pages : pages
Book Rating : 4.:/5 (12 download)

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Book Synopsis Birkhoff Interpolation Problem by : G. G. Lorentz

Download or read book Birkhoff Interpolation Problem written by G. G. Lorentz and published by . This book was released on 1975 with total page pages. Available in PDF, EPUB and Kindle. Book excerpt:

Birkhoff Interpolation Problem

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ISBN 13 :
Total Pages : pages
Book Rating : 4.:/5 (256 download)

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Book Synopsis Birkhoff Interpolation Problem by : George G. Lorentz

Download or read book Birkhoff Interpolation Problem written by George G. Lorentz and published by . This book was released on 1975 with total page pages. Available in PDF, EPUB and Kindle. Book excerpt:

Theory of Birkhoff Interpolation

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Publisher : Nova Publishers
ISBN 13 : 9781590336922
Total Pages : 266 pages
Book Rating : 4.3/5 (369 download)

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Book Synopsis Theory of Birkhoff Interpolation by : Ying Guang Shi

Download or read book Theory of Birkhoff Interpolation written by Ying Guang Shi and published by Nova Publishers. This book was released on 2003 with total page 266 pages. Available in PDF, EPUB and Kindle. Book excerpt: Interpolation by polynomials is a very old subject. The first systematic work was due to Newton in the seventeenth century. Lagrange developed his formula only a little later. In 1878 Hermie introduced so called Hermite interpolation. In 1906 Birkhoff published the first paper on lacunary (or Birkhoff) interpolation whose information about a function and its derivatives is irregular. It turns out that the Birkhoff interpolation problem is very difficult. The reasons are: the solvability of the problem is equivalent to non-singularity of the coefficient matrix of higher order, which of course is not easy to determine in general; should the solvability of the problem be known, it is difficult to get an explicit representation of the solution; although an explicit representation of the solution in some special cases can be acquired, it is usually complicated and is hard to study. This book is largely self-contained. It begins with the definitions and elementary properties of Birkhoff interpolation, to be followed by the formulating of the fundamental theorems for regularity and comparison theorems; also investigated are fundamental polynomials of interpolation in details. Interpolation follow.

Birkhoff Interpolation

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Publisher : Cambridge University Press
ISBN 13 : 9780521302395
Total Pages : 308 pages
Book Rating : 4.3/5 (23 download)

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Book Synopsis Birkhoff Interpolation by : G. G. Lorentz

Download or read book Birkhoff Interpolation written by G. G. Lorentz and published by Cambridge University Press. This book was released on 1984-12-28 with total page 308 pages. Available in PDF, EPUB and Kindle. Book excerpt: This reference book provides the main definitions, theorems and techniques in the theory of Birkhoff interpolation by polynomials. The book begins with an article by G. G. Lorentz that discusses some of the important developments in approximation and interpolation in the last twenty years. It presents all the basic material known at the present time in a unified manner. Topics discussed include; applications of Birkhoff interpolation to approximation theory, quadrature formulas and Chebyshev systems; lacunary interpolation at special knots and an introduction to the theory of Birkhoff interpolation by splines.

On Hermite-Birkhoff Interpolation

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Publisher :
ISBN 13 :
Total Pages : 11 pages
Book Rating : 4.:/5 (254 download)

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Book Synopsis On Hermite-Birkhoff Interpolation by : I. J. Schoenberg

Download or read book On Hermite-Birkhoff Interpolation written by I. J. Schoenberg and published by . This book was released on 1966 with total page 11 pages. Available in PDF, EPUB and Kindle. Book excerpt: A theorem of Polya (1931) concerning the existence of a unique polynomial solution to an interpolation problem of the kind studied by G.D. Birkhoff (1906) is generalized from Polya's case of only two nodes to a more general type of interpolation problem here described as of the quasi-Hermite type. (Author).

Frontiers in Interpolation and Approximation

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Publisher : CRC Press
ISBN 13 : 1420011383
Total Pages : 476 pages
Book Rating : 4.4/5 (2 download)

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Book Synopsis Frontiers in Interpolation and Approximation by : N. K. Govil

Download or read book Frontiers in Interpolation and Approximation written by N. K. Govil and published by CRC Press. This book was released on 2006-07-20 with total page 476 pages. Available in PDF, EPUB and Kindle. Book excerpt: 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.

An Algorithmic Approach to the General Linear Interpolation Problem with Applications to Hermite-Birkhoff-Interpolation

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Publisher :
ISBN 13 :
Total Pages : 40 pages
Book Rating : 4.:/5 (551 download)

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Book Synopsis An Algorithmic Approach to the General Linear Interpolation Problem with Applications to Hermite-Birkhoff-Interpolation by : Günter Mühlbach

Download or read book An Algorithmic Approach to the General Linear Interpolation Problem with Applications to Hermite-Birkhoff-Interpolation written by Günter Mühlbach and published by . This book was released on 1979 with total page 40 pages. Available in PDF, EPUB and Kindle. Book excerpt:

On Some Generalized Hermite-Birkhoff Interpolation Problems

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Publisher :
ISBN 13 : 9789514101502
Total Pages : 12 pages
Book Rating : 4.1/5 (15 download)

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Book Synopsis On Some Generalized Hermite-Birkhoff Interpolation Problems by : Matti Mäkelä

Download or read book On Some Generalized Hermite-Birkhoff Interpolation Problems written by Matti Mäkelä and published by . This book was released on 1974 with total page 12 pages. Available in PDF, EPUB and Kindle. Book excerpt:

Jackson-type Theorems for SAIN Approximation and the Rank of Hermite-Birkhoff Interpolation

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Publisher :
ISBN 13 :
Total Pages : 300 pages
Book Rating : 4.3/5 (121 download)

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Book Synopsis Jackson-type Theorems for SAIN Approximation and the Rank of Hermite-Birkhoff Interpolation by : Darell James Johnson

Download or read book Jackson-type Theorems for SAIN Approximation and the Rank of Hermite-Birkhoff Interpolation written by Darell James Johnson and published by . This book was released on 1972 with total page 300 pages. Available in PDF, EPUB and Kindle. Book excerpt:

Hermite-Birkhoff Interpolation Problems in Haar Subspaces

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Publisher :
ISBN 13 :
Total Pages : 24 pages
Book Rating : 4.:/5 (729 download)

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Book Synopsis Hermite-Birkhoff Interpolation Problems in Haar Subspaces by : Yasuhiko Ikebe

Download or read book Hermite-Birkhoff Interpolation Problems in Haar Subspaces written by Yasuhiko Ikebe and published by . This book was released on 1971 with total page 24 pages. Available in PDF, EPUB and Kindle. Book excerpt:

Using computer algebra to solve the birkhoff interpolation problem

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Publisher :
ISBN 13 :
Total Pages : 15 pages
Book Rating : 4.:/5 (757 download)

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Book Synopsis Using computer algebra to solve the birkhoff interpolation problem by : L. González Vega

Download or read book Using computer algebra to solve the birkhoff interpolation problem written by L. González Vega and published by . This book was released on 1995 with total page 15 pages. Available in PDF, EPUB and Kindle. Book excerpt:

Hermite-birkhoff Interpolation Problems in Haar Subspaces

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Publisher :
ISBN 13 :
Total Pages : pages
Book Rating : 4.:/5 (12 download)

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Book Synopsis Hermite-birkhoff Interpolation Problems in Haar Subspaces by : Y. Ikebe

Download or read book Hermite-birkhoff Interpolation Problems in Haar Subspaces written by Y. Ikebe and published by . This book was released on 1971 with total page pages. Available in PDF, EPUB and Kindle. Book excerpt:

Approximation with Hermite-Birkhoff Interpolatory Constraints and Related H-set Theory

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Publisher :
ISBN 13 :
Total Pages : 254 pages
Book Rating : 4.3/5 (129 download)

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Book Synopsis Approximation with Hermite-Birkhoff Interpolatory Constraints and Related H-set Theory by : Donald Marvin Platte

Download or read book Approximation with Hermite-Birkhoff Interpolatory Constraints and Related H-set Theory written by Donald Marvin Platte and published by . This book was released on 1972 with total page 254 pages. Available in PDF, EPUB and Kindle. Book excerpt:

The Question of Uniqueness for G.D. Birkoff Interpolation Problems

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Publisher :
ISBN 13 :
Total Pages : 134 pages
Book Rating : 4.:/5 (89 download)

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Book Synopsis The Question of Uniqueness for G.D. Birkoff Interpolation Problems by : David Ferguson

Download or read book The Question of Uniqueness for G.D. Birkoff Interpolation Problems written by David Ferguson and published by . This book was released on 1968 with total page 134 pages. Available in PDF, EPUB and Kindle. Book excerpt:

Applied and Computational Matrix Analysis

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Publisher : Springer
ISBN 13 : 331949984X
Total Pages : 346 pages
Book Rating : 4.3/5 (194 download)

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Book Synopsis Applied and Computational Matrix Analysis by : Natália Bebiano

Download or read book Applied and Computational Matrix Analysis written by Natália Bebiano and published by Springer. This book was released on 2017-03-01 with total page 346 pages. Available in PDF, EPUB and Kindle. Book excerpt: This volume presents recent advances in the field of matrix analysis based on contributions at the MAT-TRIAD 2015 conference. Topics covered include interval linear algebra and computational complexity, Birkhoff polynomial basis, tensors, graphs, linear pencils, K-theory and statistic inference, showing the ubiquity of matrices in different mathematical areas. With a particular focus on matrix and operator theory, statistical models and computation, the International Conference on Matrix Analysis and its Applications 2015, held in Coimbra, Portugal, was the sixth in a series of conferences. Applied and Computational Matrix Analysis will appeal to graduate students and researchers in theoretical and applied mathematics, physics and engineering who are seeking an overview of recent problems and methods in matrix analysis.

Problems in Approximation Theory

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Publisher :
ISBN 13 :
Total Pages : 170 pages
Book Rating : 4.3/5 (91 download)

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Book Synopsis Problems in Approximation Theory by : G. G. Lorentz

Download or read book Problems in Approximation Theory written by G. G. Lorentz and published by . This book was released on 1977 with total page 170 pages. Available in PDF, EPUB and Kindle. Book excerpt: