Approximation Theory: Moduli of Continuity and Global Smoothness Preservation
Gespeichert in:
| 1. Verfasser: | |
|---|---|
| Format: | Elektronisch E-Book |
| Sprache: | English |
| Veröffentlicht: |
Boston, MA
Birkhäuser Boston
2000
|
| Schlagworte: | |
| Online-Zugang: | Volltext |
| Beschreibung: | 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 values 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 Property (GSPP) for almost all known linear approximation operators of approximation theory including: trigonometric operators and algebraic interpolation operators of Lagrange, Hermite-Fejer and Shepard type, also operators of stochastic type, convolution type, wavelet type integral operators 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 mathematics such as Functional analysis, and outside of mathematics, fields such as computer-aided geometric design (CAGD). Most of the time GSPP methods 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. |
| Beschreibung: | 1 Online-Ressource (XIII, 525 p) |
| ISBN: | 9781461213604 9781461271123 |
| DOI: | 10.1007/978-1-4612-1360-4 |
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| 500 | |a 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 values 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 Property (GSPP) for almost all known linear approximation operators of approximation theory including: trigonometric operators and algebraic interpolation operators of Lagrange, Hermite-Fejer and Shepard type, also operators of stochastic type, convolution type, wavelet type integral operators 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 mathematics such as Functional analysis, and outside of mathematics, fields such as computer-aided geometric design (CAGD). Most of the time GSPP methods 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. | ||
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Datensatz im Suchindex
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| discipline | Mathematik |
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| spelling | Anastassiou, George A. 1952- Verfasser (DE-588)121815900 aut Approximation Theory Moduli of Continuity and Global Smoothness Preservation by George A. Anastassiou, Sorin G. Gal Boston, MA Birkhäuser Boston 2000 1 Online-Ressource (XIII, 525 p) txt rdacontent c rdamedia cr rdacarrier 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 values 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 Property (GSPP) for almost all known linear approximation operators of approximation theory including: trigonometric operators and algebraic interpolation operators of Lagrange, Hermite-Fejer and Shepard type, also operators of stochastic type, convolution type, wavelet type integral operators 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 mathematics such as Functional analysis, and outside of mathematics, fields such as computer-aided geometric design (CAGD). Most of the time GSPP methods 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. Mathematics Global analysis (Mathematics) Global analysis Computer science / Mathematics Applications of Mathematics Approximations and Expansions Global Analysis and Analysis on Manifolds Analysis Computational Mathematics and Numerical Analysis Informatik Mathematik Approximationstheorie (DE-588)4120913-8 gnd rswk-swf Approximationstheorie (DE-588)4120913-8 s 1\p DE-604 Gal, Sorin G. 1953- Sonstige (DE-588)1060989719 oth https://doi.org/10.1007/978-1-4612-1360-4 Verlag Volltext 1\p cgwrk 20201028 DE-101 https://d-nb.info/provenance/plan#cgwrk |
| spellingShingle | Anastassiou, George A. 1952- Approximation Theory Moduli of Continuity and Global Smoothness Preservation Mathematics Global analysis (Mathematics) Global analysis Computer science / Mathematics Applications of Mathematics Approximations and Expansions Global Analysis and Analysis on Manifolds Analysis Computational Mathematics and Numerical Analysis Informatik Mathematik Approximationstheorie (DE-588)4120913-8 gnd |
| subject_GND | (DE-588)4120913-8 |
| title | Approximation Theory Moduli of Continuity and Global Smoothness Preservation |
| title_auth | Approximation Theory Moduli of Continuity and Global Smoothness Preservation |
| title_exact_search | Approximation Theory Moduli of Continuity and Global Smoothness Preservation |
| title_full | Approximation Theory Moduli of Continuity and Global Smoothness Preservation by George A. Anastassiou, Sorin G. Gal |
| title_fullStr | Approximation Theory Moduli of Continuity and Global Smoothness Preservation by George A. Anastassiou, Sorin G. Gal |
| title_full_unstemmed | Approximation Theory Moduli of Continuity and Global Smoothness Preservation by George A. Anastassiou, Sorin G. Gal |
| title_short | Approximation Theory |
| title_sort | approximation theory moduli of continuity and global smoothness preservation |
| title_sub | Moduli of Continuity and Global Smoothness Preservation |
| topic | Mathematics Global analysis (Mathematics) Global analysis Computer science / Mathematics Applications of Mathematics Approximations and Expansions Global Analysis and Analysis on Manifolds Analysis Computational Mathematics and Numerical Analysis Informatik Mathematik Approximationstheorie (DE-588)4120913-8 gnd |
| topic_facet | Mathematics Global analysis (Mathematics) Global analysis Computer science / Mathematics Applications of Mathematics Approximations and Expansions Global Analysis and Analysis on Manifolds Analysis Computational Mathematics and Numerical Analysis Informatik Mathematik Approximationstheorie |
| url | https://doi.org/10.1007/978-1-4612-1360-4 |
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