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Record Nr. |
UNINA9910136914703321 |
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Autore |
Celant Giorgio |
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Titolo |
Interpolation and extrapolation optimal designs 1 : polynomial regression and approximation theory / / Giorgio Celant, Michel Broniatowski |
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Pubbl/distr/stampa |
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London, England ; ; Hoboken, New Jersey : , : iSTE : , : Wiley, , 2016 |
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©2016 |
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ISBN |
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1-119-29229-8 |
1-119-29228-X |
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Descrizione fisica |
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1 online resource (266 p.) |
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Collana |
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Mathematics and Statistics |
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Disciplina |
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Soggetti |
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Interpolation |
Approximation theory |
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Lingua di pubblicazione |
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Formato |
Materiale a stampa |
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Livello bibliografico |
Monografia |
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Note generali |
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Description based upon print version of record. |
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Nota di bibliografia |
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Includes bibliographical references and index. |
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Nota di contenuto |
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Table of Contents; Title; Copyright; Preface; Introduction; I.1. The scope of this book; I.2. A generic case: the Hoel and Levine extrapolation scheme and the uniform interpolation design of Guest; I.3. Extrapolation design in non standard cases, algorithms; I.4. Uniform approximation of functions, an outlook; I.5. A general bibliography; PART 1: Elements from Approximation Theory; 1 Uniform Approximation; 1.1. Canonical polynomials and uniform approximation; 1.2. Existence of the best approximation; 1.3. Characterization and uniqueness of the best approximation |
2 Convergence Rates for the Uniform Approximation and Algorithms2.1. Introduction; 2.2. The Borel-Chebyshev theorem and standard functions; 2.3. Convergence of the minimax approximation; 2.4. Proof of the de la Vallée Poussin theorem; 2.5. The Yevgeny Yakovlevich Remez algorithm; 3 Constrained Polynomial Approximation; 3.1. Introduction and examples; 3.2. Lagrange polynomial interpolation; 3.3. The interpolation error; 3.4. The role of the nodes and the minimization of the interpolation error; 3.5. Convergence of the interpolation approximation; 3.6. Runge phenomenon and lack of convergence |
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