Approximation Theory Xvi
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Author |
: Gregory E. Fasshauer |
Publisher |
: Springer Nature |
Total Pages |
: 256 |
Release |
: 2021-01-04 |
ISBN-10 |
: 9783030574642 |
ISBN-13 |
: 3030574644 |
Rating |
: 4/5 (42 Downloads) |
Synopsis Approximation Theory XVI by : Gregory E. Fasshauer
These proceedings are based on the international conference Approximation Theory XVI held on May 19–22, 2019 in Nashville, Tennessee. The conference was the sixteenth in a series of meetings in Approximation Theory held at various locations in the United States. Over 130 mathematicians from 20 countries attended. The book contains two longer survey papers on nonstationary subdivision and Prony’s method, along with 11 research papers on a variety of topics in approximation theory, including Balian-Low theorems, butterfly spline interpolation, cubature rules, Hankel and Toeplitz matrices, phase retrieval, positive definite kernels, quasi-interpolation operators, stochastic collocation, the gradient conjecture, time-variant systems, and trivariate finite elements. The book should be of interest to mathematicians, engineers, and computer scientists working in approximation theory, computer-aided geometric design, numerical analysis, and related approximation areas.
Author |
: Gregory E. Fasshauer |
Publisher |
: |
Total Pages |
: 0 |
Release |
: 2021 |
ISBN-10 |
: 3030574652 |
ISBN-13 |
: 9783030574659 |
Rating |
: 4/5 (52 Downloads) |
Synopsis Approximation Theory XVI by : Gregory E. Fasshauer
These proceedings are based on the international conference Approximation Theory XVI held on May 19-22, 2019 in Nashville, Tennessee. The conference was the sixteenth in a series of meetings in Approximation Theory held at various locations in the United States. Over 130 mathematicians from 20 countries attended. The book contains two longer survey papers on nonstationary subdivision and Prony's method, along with 11 research papers on a variety of topics in approximation theory, including Balian-Low theorems, butterfly spline interpolation, cubature rules, Hankel and Toeplitz matrices, phase retrieval, positive definite kernels, quasi-interpolation operators, stochastic collocation, the gradient conjecture, time-variant systems, and trivariate finite elements. The book should be of interest to mathematicians, engineers, and computer scientists working in approximation theory, computer-aided geometric design, numerical analysis, and related approximation areas.
Author |
: Narenda Govil |
Publisher |
: CRC Press |
Total Pages |
: 548 |
Release |
: 2021-01-31 |
ISBN-10 |
: 9781000110180 |
ISBN-13 |
: 1000110184 |
Rating |
: 4/5 (80 Downloads) |
Synopsis Approximation Theory by : Narenda Govil
"Contains the contributions of 45 internationally distinguished mathematicians covering all areas of approximation theory-written in honor of the pioneering work of Arun K. Varma to the fields of interpolation and approximation of functions, including Birhoff interpolation and approximation by spline functions."
Author |
: M. J. D. Powell |
Publisher |
: Cambridge University Press |
Total Pages |
: 356 |
Release |
: 1981-03-31 |
ISBN-10 |
: 0521295149 |
ISBN-13 |
: 9780521295147 |
Rating |
: 4/5 (49 Downloads) |
Synopsis Approximation Theory and Methods by : M. J. D. Powell
Most functions that occur in mathematics cannot be used directly in computer calculations. Instead they are approximated by manageable functions such as polynomials and piecewise polynomials. The general theory of the subject and its application to polynomial approximation are classical, but piecewise polynomials have become far more useful during the last twenty years. Thus many important theoretical properties have been found recently and many new techniques for the automatic calculation of approximations to prescribed accuracy have been developed. This book gives a thorough and coherent introduction to the theory that is the basis of current approximation methods. Professor Powell describes and analyses the main techniques of calculation supplying sufficient motivation throughout the book to make it accessible to scientists and engineers who require approximation methods for practical needs. Because the book is based on a course of lectures to third-year undergraduates in mathematics at Cambridge University, sufficient attention is given to theory to make it highly suitable as a mathematical textbook at undergraduate or postgraduate level.
Author |
: Carl De Boor |
Publisher |
: American Mathematical Soc. |
Total Pages |
: 145 |
Release |
: 1986 |
ISBN-10 |
: 9780821800980 |
ISBN-13 |
: 0821800981 |
Rating |
: 4/5 (80 Downloads) |
Synopsis Approximation Theory by : Carl De Boor
Presented at a 1986 AMS Short Course, this title contains papers that give a brief introduction to approximation theory and some of its areas of active research, both theoretical and applied. It is best understood by those with a standard first graduate course in real and complex analysis.
Author |
: Karl-Georg Steffens |
Publisher |
: Springer Science & Business Media |
Total Pages |
: 219 |
Release |
: 2007-07-28 |
ISBN-10 |
: 9780817644758 |
ISBN-13 |
: 081764475X |
Rating |
: 4/5 (58 Downloads) |
Synopsis The History of Approximation Theory by : Karl-Georg Steffens
* Exciting exposition integrates history, philosophy, and mathematics * Combines a mathematical analysis of approximation theory with an engaging discussion of the differing philosophical underpinnings behind its development * Appendices containing biographical data on numerous eminent mathematicians, explanations of Russian nomenclature and academic degrees, and an excellent index round out the presentation
Author |
: E. W. Cheney |
Publisher |
: SIAM |
Total Pages |
: 74 |
Release |
: 1986-01-01 |
ISBN-10 |
: 1611970199 |
ISBN-13 |
: 9781611970197 |
Rating |
: 4/5 (99 Downloads) |
Synopsis Multivariate Approximation Theory by : E. W. Cheney
The approximation of functions of several variables continues to be a difficult problem in scientific computing because many of the algorithms required for such problems have yet to be written. This monograph is written for a broad audience of computational mathematicians and statisticians concerned with the development of algorithms or the derivation of approximations from linear projections, of which the interpolating operators are an important example. As an aid to both researchers and students, a bibliography of more than 200 titles is included.
Author |
: Javad Mashreghi |
Publisher |
: Springer |
Total Pages |
: 277 |
Release |
: 2018-03-28 |
ISBN-10 |
: 9781493975433 |
ISBN-13 |
: 1493975439 |
Rating |
: 4/5 (33 Downloads) |
Synopsis New Trends in Approximation Theory by : Javad Mashreghi
The international conference entitled "New Trends in Approximation Theory" was held at the Fields Institute, in Toronto, from July 25 until July 29, 2016. The conference was fondly dedicated to the memory of our unique friend and colleague, André Boivin, who gave tireless service in Canada until his very last moment of his life in October 2014. The impact of his warm personality and his fine work on Complex Approximation Theory was reflected by the mathematical excellence and the wide research range of the 37 participants. In total there were 27 talks, delivered by well-established mathematicians and young researchers. In particular, 19 invited lectures were delivered by leading experts of the field, from 8 different countries. The wide variety of presentations composed a mosaic of aspects of approximation theory, highlighting interesting connections with important contemporary areas of Analysis. Primary topics discussed include application of approximation theory (isoperimetric inequalities, construction of entire order-isomorphisms, dynamical sampling); approximation by harmonic and holomorphic functions (especially uniform and tangential approximation), polynomial and rational approximation; zeros of approximants and zero-free approximation; tools used in approximation theory; approximation on complex manifolds, in product domains, and in function spaces; and boundary behaviour and universality properties of Taylor and Dirichlet series.
Author |
: George A. Anastassiou |
Publisher |
: Springer Science & Business Media |
Total Pages |
: 520 |
Release |
: 2012-12-06 |
ISBN-10 |
: 9781461213604 |
ISBN-13 |
: 1461213606 |
Rating |
: 4/5 (04 Downloads) |
Synopsis Approximation Theory by : George A. Anastassiou
We study in Part I of this monograph the computational aspect of almost all moduli of continuity over wide classes of functions exploiting some of their convexity properties. To our knowledge it is the first time the entire calculus of moduli of smoothness has been included in a book. We then present numerous applications of Approximation Theory, giving exact val ues of errors in explicit forms. The K-functional method is systematically avoided since it produces nonexplicit constants. All other related books so far have allocated very little space to the computational aspect of moduli of smoothness. In Part II, we study/examine the Global Smoothness Preservation Prop erty (GSPP) for almost all known linear approximation operators of ap proximation theory including: trigonometric operators and algebraic in terpolation operators of Lagrange, Hermite-Fejer and Shepard type, also operators of stochastic type, convolution type, wavelet type integral opera tors and singular integral operators, etc. We present also a sufficient general theory for GSPP to hold true. We provide a great variety of applications of GSPP to Approximation Theory and many other fields of mathemat ics such as Functional analysis, and outside of mathematics, fields such as computer-aided geometric design (CAGD). Most of the time GSPP meth ods are optimal. Various moduli of smoothness are intensively involved in Part II. Therefore, methods from Part I can be used to calculate exactly the error of global smoothness preservation. It is the first time in the literature that a book has studied GSPP.
Author |
: Elliott Ward Cheney |
Publisher |
: Thomson Brooks/Cole |
Total Pages |
: 396 |
Release |
: 2000 |
ISBN-10 |
: UOM:39076002389828 |
ISBN-13 |
: |
Rating |
: 4/5 (28 Downloads) |
Synopsis A Course in Approximation Theory by : Elliott Ward Cheney
1. Introductory Discussion of Interpolation 2. Linear Interpolation Operators 3. Optimization of the Lagrange Operator 4. Multivariate Polynomials 5. Moving the Nodes 6. Projections 7. Tensor Product Interpolation 8. The Boolean Algebra of Projections 9. The Newton Paradigm for Interpolation 10. The Lagrange Paradigm for Interpolation 11. Interpolation by Translates of a Single Function 12. Positive Definite Functions 13. Strictly Positive Definite Functions 14. Completely Monotone Functions 15. The Schoenberg Interpolation Theorem 16. The Micchelli Interpolation Theorem 17. Positive Definite Functions of Spheres 18. Approximation by Positive Definite Functions 19. Approximate Reconstruction of Functions and Tomography 20. Approximation by Convolution 21. The Good Kernels 22. Ridge Functions 23. Ridge Function Approximation via Convolutions 24. Density of Ridge Functions 25. Artificial Neural Networks 26. Chebyshev Centers 27. Optimal Reconstruction of Functions 28. Algorithmic Orthogonal Projections 29. Cardinal B-Splines and the Sinc Function 30. The Golomb-Weinberger Theory 31. Hilbert Function Spaces, Reproducing Kernels 32. Spherical Splines 33. Box Splines 34. Wavelets, Part I 35. Wavelets, Part II 36. Quasi-Interpolation Bibliography / Index