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Author: Nikolaĭ Pavlovich Korneĭchuk
Publisher: Nova Publishers
ISBN: 9781560723615
Category : Mathematics
Languages : en
Pages : 444
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Book Description
Extremal Properties of Polynomials & Splines
Author: Nikolaĭ Pavlovich Korneĭchuk
Publisher: Nova Publishers
ISBN: 9781560723615
Category : Mathematics
Languages : en
Pages : 444
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Book Description
Extremal Properties of Polynomials & Splines
Author: Borislav D. Bojanov
Publisher: Springer
ISBN: 9789401581707
Category : Mathematics
Languages : en
Pages : 278
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Book Description
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.
Author: S. B. Stechkin
Publisher: American Mathematical Soc.
ISBN: 9780821830499
Category : Mathematics
Languages : en
Pages : 280
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Book Description
Papers and articles about polynomials and splines pproximation.
Author: G. V. Milovanovi?
Publisher: World Scientific
ISBN: 9789810204990
Category : Science
Languages : en
Pages : 842
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Book Description
The book contains some of the most important results on the analysis of polynomials and their derivatives. Besides the fundamental results which are treated with their proofs, the book also provides an account of the most recent developments concerning extremal properties of polynomials and their derivatives in various metrics with an extensive analysis of inequalities for trigonometric sums and algebraic polynomials, as well as their zeros. The final chapter provides some selected applications of polynomials in approximation theory and computer aided geometric design (CAGD). One can also find in this book several new research problems and conjectures with sufficient information concerning the results obtained to date towards the investigation of their solution.
Author: S. B. Stechkin
Publisher:
ISBN:
Category : Mathematics
Languages : en
Pages : 380
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Book Description
Proceedings and papers discussing properties of polynomials.
Author: B.N. Sahney
Publisher: Springer
ISBN:
Category : Mathematics
Languages : en
Pages : 344
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Book Description
Proceedings of the NATO Advanced Study Institute, Calgary, Canada, August 26-September 2, 1978
Author: Borislav D. Bojanov
Publisher: Springer
ISBN: 9780792322290
Category : Computers
Languages : en
Pages : 292
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Book Description
This volume provides a comprehensive introduction to the theory of spline functions. Emphasis is given to new developments, such as the general Birkhoff-type interpolation, the extremal properties of splines, their prominent role in the optimal recovery of functions, and multivariate interpolation by polynomials and splines. The book has thirteen chapters dealing, respectively, with interpolation by algebraic polynomials, the space of splines, B-splines, interpolation by spline functions, natural spline functions, perfect splines, monosplines, periodic splines, multivariate B-splines and truncated powers, multivariate spline functions and divided differences, box splines, multivariate mean value interpolation, multivariate polynomial interpolations arising by hyperplanes, and multivariate pointwise interpolation. Some of the results described are presented as exercises and hints are given for their solution. For researchers and graduate students whose work involves approximation theory.
Author: Kenneth Ownsworth May
Publisher:
ISBN:
Category :
Languages : en
Pages :
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Book Description
Author: J. L. Walsh
Publisher:
ISBN:
Category : Extremal problems (Mathematics)
Languages : en
Pages : 32
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Book Description
Author: Gradimir V Milovanovic
Publisher: World Scientific
ISBN: 9814506486
Category : Science
Languages : en
Pages : 844
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Book Description
The book contains some of the most important results on the analysis of polynomials and their derivatives. Besides the fundamental results which are treated with their proofs, the book also provides an account of the most recent developments concerning extremal properties of polynomials and their derivatives in various metrics with an extensive analysis of inequalities for trigonometric sums and algebraic polynomials, as well as their zeros. The final chapter provides some selected applications of polynomials in approximation theory and computer aided geometric design (CAGD). One can also find in this book several new research problems and conjectures with sufficient information concerning the results obtained to date towards the investigation of their solution.
