Multivariate Approximation And Interpolation

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Topics in Multivariate Approximation and Interpolation

Author : Kurt Jetter
Publisher : Elsevier
ISBN 13 : 0080462049
Total Pages : 357 pages
Book Rating : 4.0/5 (84 download)

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Book Synopsis Topics in Multivariate Approximation and Interpolation by : Kurt Jetter

Download or read book Topics in Multivariate Approximation and Interpolation written by Kurt Jetter and published by Elsevier. This book was released on 2005-11-15 with total page 357 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book is a collection of eleven articles, written by leading experts and dealing with special topics in Multivariate Approximation and Interpolation. The material discussed here has far-reaching applications in many areas of Applied Mathematics, such as in Computer Aided Geometric Design, in Mathematical Modelling, in Signal and Image Processing and in Machine Learning, to mention a few. The book aims at giving a comprehensive information leading the reader from the fundamental notions and results of each field to the forefront of research. It is an ideal and up-to-date introduction for graduate students specializing in these topics, and for researchers in universities and in industry. A collection of articles of highest scientific standard An excellent introduction and overview of recent topics from multivariate approximation A valuable source of references for specialists in the field A representation of the state-of-the-art in selected areas of multivariate approximation A rigorous mathematical introduction to special topics of interdisciplinary research

Topics in Multivariate Approximation

Author : C. K. Chui
Publisher : Elsevier
ISBN 13 : 1483271005
Total Pages : 346 pages
Book Rating : 4.4/5 (832 download)

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Book Synopsis Topics in Multivariate Approximation by : C. K. Chui

Download or read book Topics in Multivariate Approximation written by C. K. Chui and published by Elsevier. This book was released on 2014-05-10 with total page 346 pages. Available in PDF, EPUB and Kindle. Book excerpt: Topics in Multivariate Approximation contains the proceedings of an international workshop on multivariate approximation held at the University of Chile in Santiago, Chile, on December 15-19, 1986. Leading researchers in the field discussed several problem areas related to multivariate approximation and tackled topics ranging from multivariate splines and fitting of scattered data to tensor approximation methods and multivariate polynomial approximation. Numerical grid generation and finite element methods were also explored, along with constrained interpolation and smoothing. Comprised of 22 chapters, this book first describes the application of Boolean methods of approximation in combination with the theory of right invertible operators to bivariate Fourier expansions. The reader is then introduced to ill-posed problems in multivariate approximation; interpolation of scattered data by radial functions; and shape-preserving surface interpolation. Subsequent chapters focus on approximation by harmonic functions; numerical generation of nested series of general triangular grids; triangulation methods; and inequalities arising from best local approximations in rectangles. A bibliography of multivariate approximation concludes the book. This monograph will be of interest to mathematicians.

Multivariate Approximation and Interpolation

Author : HAUSMANN
Publisher : Springer-Verlag
ISBN 13 : 3034856857
Total Pages : 331 pages
Book Rating : 4.0/5 (348 download)

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Book Synopsis Multivariate Approximation and Interpolation by : HAUSMANN

Download or read book Multivariate Approximation and Interpolation written by HAUSMANN and published by Springer-Verlag. This book was released on 2013-11-21 with total page 331 pages. Available in PDF, EPUB and Kindle. Book excerpt:

Multivariate Approximation: From CAGD to Wavelets

Author : K Jetter
Publisher : World Scientific
ISBN 13 : 9814602523
Total Pages : 348 pages
Book Rating : 4.8/5 (146 download)

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Book Synopsis Multivariate Approximation: From CAGD to Wavelets by : K Jetter

Download or read book Multivariate Approximation: From CAGD to Wavelets written by K Jetter and published by World Scientific. This book was released on 1993-11-30 with total page 348 pages. Available in PDF, EPUB and Kindle. Book excerpt: Contents: Fast Algorithms for Simultaneous Polynomial Approximation (G Baszenski & M Tasche)α-Spline of Smoothing for Correlated Errors in Dimension Two (M Bozzini & L Lenarduzzi)New Developments in the Theory of Radial Basis Function Interpolation (M D Buhmann)Realization of Neural Networks with One Hidden Layer (C K Chui & X Li)A General Method for Constrained Curves with Boundary Conditions (P Costantini)Sign-Regular and Totally Positive Matrices: An Algorithmic Approach (M Gasca & J M Peña)Some Results on Blossoming and Multivariate B-Splines (R Gormaz & P-J Laurent)Riesz Bounds in Scattered Data Interpolation and L2-Approximation (K Jetter)On Multivariate Hermite Polynomial Interpolation (A Le Méhauté)Quantitative Approximation Results for Sigma-Pi-Type Neural Network Operators (B Lenze)Local Interpolation Schemes — From Curves to Surfaces (D Levin)Some Results on Approximation by Smoothing Dm-Splines (M C L de Silanes) Readership: Applied mathematicians.

Multivariate Approximation and Splines

Author : Günther Nürnberger
Publisher : Birkhäuser
ISBN 13 : 3034888716
Total Pages : 329 pages
Book Rating : 4.0/5 (348 download)

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Book Synopsis Multivariate Approximation and Splines by : Günther Nürnberger

Download or read book Multivariate Approximation and Splines written by Günther Nürnberger and published by Birkhäuser. This book was released on 2012-12-06 with total page 329 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book contains the refereed papers which were presented at the interna tional conference on "Multivariate Approximation and Splines" held in Mannheim, Germany, on September 7-10,1996. Fifty experts from Bulgaria, England, France, Israel, Netherlands, Norway, Poland, Switzerland, Ukraine, USA and Germany participated in the symposium. It was the aim of the conference to give an overview of recent developments in multivariate approximation with special emphasis on spline methods. The field is characterized by rapidly developing branches such as approximation, data fit ting, interpolation, splines, radial basis functions, neural networks, computer aided design methods, subdivision algorithms and wavelets. The research has applications in areas like industrial production, visualization, pattern recognition, image and signal processing, cognitive systems and modeling in geology, physics, biology and medicine. In the following, we briefly describe the contents of the papers. Exact inequalities of Kolmogorov type which estimate the derivatives of mul the paper of BABENKO, KOFANovand tivariate periodic functions are derived in PICHUGOV. These inequalities are applied to the approximation of classes of mul tivariate periodic functions and to the approximation by quasi-polynomials. BAINOV, DISHLIEV and HRISTOVA investigate initial value problems for non linear impulse differential-difference equations which have many applications in simulating real processes. By applying iterative techniques, sequences of lower and upper solutions are constructed which converge to a solution of the initial value problem.

Multivariate Polynomial Approximation

Author : Manfred Reimer
Publisher : Birkhäuser
ISBN 13 : 3034880952
Total Pages : 361 pages
Book Rating : 4.0/5 (348 download)

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Book Synopsis Multivariate Polynomial Approximation by : Manfred Reimer

Download or read book Multivariate Polynomial Approximation written by Manfred Reimer and published by Birkhäuser. This book was released on 2012-12-06 with total page 361 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book introduces general theory by presenting the most important facts on multivariate interpolation, quadrature, orthogonal projections and their summation, all treated under a constructive view, and embedded in the theory of positive linear operators. On this background, the book builds the first comprehensive introduction to the theory of generalized hyperinterpolation. Several parts of the book are based on rotation principles, which are presented in the beginning of the book.

Interpolation and Approximation by Polynomials

Author : George M. Phillips
Publisher : Springer Science & Business Media
ISBN 13 : 0387216820
Total Pages : 325 pages
Book Rating : 4.3/5 (872 download)

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Book Synopsis Interpolation and Approximation by Polynomials by : George M. Phillips

Download or read book Interpolation and Approximation by Polynomials written by George M. Phillips and published by Springer Science & Business Media. This book was released on 2006-04-06 with total page 325 pages. Available in PDF, EPUB and Kindle. Book excerpt: In addition to coverage of univariate interpolation and approximation, the text includes material on multivariate interpolation and multivariate numerical integration, a generalization of the Bernstein polynomials that has not previously appeared in book form, and a greater coverage of Peano kernel theory than is found in most textbooks. There are many worked examples and each section ends with a number of carefully selected problems that extend the student's understanding of the text. The author is well known for his clarity of writing and his many contributions as a researcher in approximation theory.

Multivariate Approximation and Interpolation

Author : Werner Haussmann
Publisher : Birkhauser
ISBN 13 : 9780817624507
Total Pages : 324 pages
Book Rating : 4.6/5 (245 download)

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Book Synopsis Multivariate Approximation and Interpolation by : Werner Haussmann

Download or read book Multivariate Approximation and Interpolation written by Werner Haussmann and published by Birkhauser. This book was released on 1990 with total page 324 pages. Available in PDF, EPUB and Kindle. Book excerpt:

Spline Functions and Multivariate Interpolations

Author : Borislav D. Bojanov
Publisher : Springer Science & Business Media
ISBN 13 : 940158169X
Total Pages : 287 pages
Book Rating : 4.4/5 (15 download)

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Book Synopsis Spline Functions and Multivariate Interpolations by : Borislav D. Bojanov

Download or read book Spline Functions and Multivariate Interpolations written by Borislav D. Bojanov and published by Springer Science & Business Media. This book was released on 2013-06-29 with total page 287 pages. Available in PDF, EPUB and Kindle. Book excerpt: Spline functions entered Approximation Theory as solutions of natural extremal problems. A typical example is the problem of drawing a function curve through given n + k points that has a minimal norm of its k-th derivative. Isolated facts about the functions, now called splines, can be found in the papers of L. Euler, A. Lebesgue, G. Birkhoff, J. Favard, L. Tschakaloff. However, the Theory of Spline Functions has developed in the last 30 years by the effort of dozens of mathematicians. Recent fundamental results on multivariate polynomial interpolation and multivari ate splines have initiated a new wave of theoretical investigations and variety of applications. The purpose of this book is to introduce the reader to the theory of spline functions. The emphasis is given to some new developments, such as the general Birkoff's type interpolation, the extremal properties of the splines and their prominant role in the optimal recovery of functions, multivariate interpolation by polynomials and splines. The material presented is based on the lectures of the authors, given to the students at the University of Sofia and Yerevan University during the last 10 years. Some more elementary results are left as excercises and detailed hints are given.

Multivariate Approximation Theory

Author : E. W. Cheney
Publisher : SIAM
ISBN 13 : 0898712076
Total Pages : 74 pages
Book Rating : 4.8/5 (987 download)

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Book Synopsis Multivariate Approximation Theory by : E. W. Cheney

Download or read book Multivariate Approximation Theory written by E. W. Cheney and published by SIAM. This book was released on 1986-10-01 with total page 74 pages. Available in PDF, EPUB and Kindle. Book excerpt: This monograph deals with the development of algorithms or the derivation of approximations from linear projections.

Multivariate Approximation

Author : V. Temlyakov
Publisher : Cambridge University Press
ISBN 13 : 1108428754
Total Pages : 551 pages
Book Rating : 4.1/5 (84 download)

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Book Synopsis Multivariate Approximation by : V. Temlyakov

Download or read book Multivariate Approximation written by V. Temlyakov and published by Cambridge University Press. This book was released on 2018-07-19 with total page 551 pages. Available in PDF, EPUB and Kindle. Book excerpt: Self-contained presentation of multivariate approximation from classical linear approximation to contemporary nonlinear approximation.

Spline Functions and Multivariate Interpolations

Author : Borislav D. Bojanov
Publisher : Springer
ISBN 13 : 9789401581707
Total Pages : 278 pages
Book Rating : 4.5/5 (817 download)

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Book Synopsis Spline Functions and Multivariate Interpolations by : Borislav D. Bojanov

Download or read book Spline Functions and Multivariate Interpolations written by Borislav D. Bojanov and published by Springer. This book was released on 2014-03-14 with total page 278 pages. Available in PDF, EPUB and Kindle. Book excerpt: Spline functions entered Approximation Theory as solutions of natural extremal problems. A typical example is the problem of drawing a function curve through given n + k points that has a minimal norm of its k-th derivative. Isolated facts about the functions, now called splines, can be found in the papers of L. Euler, A. Lebesgue, G. Birkhoff, J. Favard, L. Tschakaloff. However, the Theory of Spline Functions has developed in the last 30 years by the effort of dozens of mathematicians. Recent fundamental results on multivariate polynomial interpolation and multivari ate splines have initiated a new wave of theoretical investigations and variety of applications. The purpose of this book is to introduce the reader to the theory of spline functions. The emphasis is given to some new developments, such as the general Birkoff's type interpolation, the extremal properties of the splines and their prominant role in the optimal recovery of functions, multivariate interpolation by polynomials and splines. The material presented is based on the lectures of the authors, given to the students at the University of Sofia and Yerevan University during the last 10 years. Some more elementary results are left as excercises and detailed hints are given.

Multivariate Splines

Author : Charles K. Chui
Publisher : SIAM
ISBN 13 : 0898712262
Total Pages : 192 pages
Book Rating : 4.8/5 (987 download)

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Book Synopsis Multivariate Splines by : Charles K. Chui

Download or read book Multivariate Splines written by Charles K. Chui and published by SIAM. This book was released on 1988-01-01 with total page 192 pages. Available in PDF, EPUB and Kindle. Book excerpt: Subject of multivariate splines presented from an elementary point of view; includes many open problems.

Recent Progress in Multivariate Approximation

Author : Werner Haussmann
Publisher : Birkhäuser
ISBN 13 : 3034882726
Total Pages : 258 pages
Book Rating : 4.0/5 (348 download)

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Book Synopsis Recent Progress in Multivariate Approximation by : Werner Haussmann

Download or read book Recent Progress in Multivariate Approximation written by Werner Haussmann and published by Birkhäuser. This book was released on 2012-12-06 with total page 258 pages. Available in PDF, EPUB and Kindle. Book excerpt: Nineteen contributions cover recent topics in constructive approximation on varieties, approximation by solutions of partial differential equations, application of Riesz bases and frames, multiwavelets and subdivision. An essential resource for researchers and graduates in applied mathematics, computer science and geophysics who are interested in the state-of-the-art developments in multivariate approximation.

Multivariate Birkhoff Interpolation

Author : Rudolph A. Lorentz
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.

Approximation Theory Viii - Volume 1: Approximation And Interpolation

Author : Charles K Chui
Publisher : World Scientific
ISBN 13 : 9814549061
Total Pages : 606 pages
Book Rating : 4.8/5 (145 download)

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Book Synopsis Approximation Theory Viii - Volume 1: Approximation And Interpolation by : Charles K Chui

Download or read book Approximation Theory Viii - Volume 1: Approximation And Interpolation written by Charles K Chui and published by World Scientific. This book was released on 1995-11-07 with total page 606 pages. Available in PDF, EPUB and Kindle. Book excerpt: This is the collection of the refereed and edited papers presented at the 8th Texas International Conference on Approximation Theory. It is interdisciplinary in nature and consists of two volumes. The central theme of Vol. I is the core of approximation theory. It includes such important areas as qualitative approximations, interpolation theory, rational approximations, radial-basis functions, and splines. The second volume focuses on topics related to wavelet analysis, including multiresolution and multi-level approximation, subdivision schemes in CAGD, and applications.

Advances in Multivariate Approximation

Author : Werner Haußmann
Publisher : Wiley-VCH
ISBN 13 :
Total Pages : 344 pages
Book Rating : 4.3/5 (91 download)

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Book Synopsis Advances in Multivariate Approximation by : Werner Haußmann

Download or read book Advances in Multivariate Approximation written by Werner Haußmann and published by Wiley-VCH. This book was released on 1999-11-12 with total page 344 pages. Available in PDF, EPUB and Kindle. Book excerpt: This volume deals with main results of the 3rd International Conference on Multivariate Approximation, organized by the University of Dortmund. Special emphasis is put on the following topics: Interpolation and approximation on spheres and balls, approximation by solutions of differential equations, construction of node systems, scattered data techniques.