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Synopsis
"Going over the introduction, the reader will get an almost full account, without proofs, of the results presented in the monograph... There are many questions for further research arising from this interesting book. Some of them are formulated by the authors, but many more may be born in the mind of the reader.” ---Zentralblatt
This monograph, in two parts, is an intensive and comprehensive study of the computational aspects of the moduli of smoothness and the Global Smoothness Preservation Property (GSPP).
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Présentation de l'éditeur
Contains the proceedings of the March 1991 annual conference of the Southeastern Approximation Theorists, in Memphis, Tenn. The 34 papers discuss topics of interest to graduate and professional numerical analysts, applied and industrial mathematicians, engineers, and other scientists such as splines
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Approximation Theory: Moduli of Continuity and Global Smoothness Preservation
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Approximation Theory : Moduli of Continuity and Global Smoothness Preservation
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Approximation Theory (Paperback)
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Paperback. Etat : new. Paperback. 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. 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 valA 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 PropA erty (GSPP) for almost all known linear approximation operators of apA proximation theory including: trigonometric operators and algebraic inA terpolation operators of Lagrange, Hermite-Fejer and Shepard type, also operators of stochastic type, convolution type, wavelet type integral operaA 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 mathematA ics such as Functional analysis, and outside of mathematics, fields such as computer-aided geometric design (CAGD). Most of the time GSPP methA 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 studie Shipping may be from multiple locations in the US or from the UK, depending on stock availability. N° de réf. du vendeur 9781461271123
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Approximation Theory: Moduli of Continuity and Global Smoothness Preservation
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Approximation Theory : Moduli of Continuity and Global Smoothness Preservation
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ISBN 10 : 1461271126
ISBN 13 : 9781461271123
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Approximation Theory: Moduli of Continuity and Global Smoothness Preservation
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Approximation Theory
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Birkhäuser Boston Okt 2012, 2012
ISBN 10 : 1461271126
ISBN 13 : 9781461271123
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Taschenbuch. Etat : Neu. This item is printed on demand - it takes 3-4 days longer - Neuware -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. 544 pp. Englisch. N° de réf. du vendeur 9781461271123
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Approximation Theory
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Birkhäuser Boston, 2012
ISBN 10 : 1461271126
ISBN 13 : 9781461271123
Neuf
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Etat : New. Dieser Artikel ist ein Print on Demand Artikel und wird nach Ihrer Bestellung fuer Sie gedruckt. 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 . N° de réf. du vendeur 4189742
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Approximation Theory
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Approximation Theory: Moduli of Continuity and Global Smoothness Preservation
Edité par
Springer-Verlag New York Inc., 2012
ISBN 10 : 1461271126
ISBN 13 : 9781461271123
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