LEADER 04035nam 2200589 450 001 9910820452703321 005 20230808192419.0 010 $a1-119-29229-8 010 $a1-119-29228-X 035 $a(CKB)3710000000635775 035 $a(EBL)4470886 035 $a(OCoLC)948395179 035 $a(MiAaPQ)EBC4470886 035 $a(Au-PeEL)EBL4470886 035 $a(CaPaEBR)ebr11203680 035 $a(CaONFJC)MIL910407 035 $a(EXLCZ)993710000000635775 100 $a20160430h20162016 uy 0 101 0 $aeng 135 $aur|n|---||||| 181 $2rdacontent 182 $2rdamedia 183 $2rdacarrier 200 10$aInterpolation and extrapolation optimal designs 1 $epolynomial regression and approximation theory /$fGiorgio Celant, Michel Broniatowski 210 1$aLondon, England ;$aHoboken, New Jersey :$ciSTE :$cWiley,$d2016. 210 4$dİ2016 215 $a1 online resource (266 p.) 225 1 $aMathematics and Statistics 300 $aDescription based upon print version of record. 311 $a1-119-29227-1 311 $a1-84821-995-4 320 $aIncludes bibliographical references and index. 327 $aTable 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 327 $a2 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 Valle?e 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 327 $a5 An Introduction to Extrapolation Problems Based on Observations on a Collection of Intervals5.1. Introduction; 5.2. The model, the estimator and the criterion for the choice of the design; 5.3. A constrained Borel-Chebyshev theorem; 5.4. Qualitative properties of the polynomial which determines the optimal nodes; 5.5. Identification of the polynomial which characterizes the optimal nodes; 5.6. The optimal design in favorable cases; 5.7. The optimal design in the general case; 5.8. Spruill theorem: the optimal design 327 $a6 Instability of the Lagrange Interpolation Scheme With Respect to Measurement Errors6.1. Introduction; 6.2. The errors that cannot be avoided; 6.3. Control of the relative errors; 6.4. Randomness; 6.5. Some inequalities for the derivatives of polynomials; 6.6. Concentration inequalities; 6.7. Upper bounds of the extrapolation error due to randomness, and the resulting size of the design for real analytic regression functions; PART 3: Mathematical Material; Appendix 1: Normed Linear Spaces; A1.1. General notions 327 $aA1.2. Compatibility between the topological and the linear structure in linear spaces 410 0$aMathematics and statistics series (ISTE) 606 $aInterpolation 606 $aApproximation theory 615 0$aInterpolation. 615 0$aApproximation theory. 676 $a511.42 700 $aCelant$b Giorgio$01596228 702 $aBroniatowski$b Michel 801 0$bMiAaPQ 801 1$bMiAaPQ 801 2$bMiAaPQ 906 $aBOOK 912 $a9910820452703321 996 $aInterpolation and extrapolation optimal designs 1$93917518 997 $aUNINA