Celant G., Broniatowski M. Interpolation and extrapolation optimal designs. 1: Polynomial regression and approximation theory

Wiley-ISTE, 2016. — 286 p. — ISBN: 1848219954, 9781848219953, 9781119292272, 1119292271, 9781119292296, 1119292298This book is the first of a series which focuses on the interpolation and extrapolation of optimal designs, an area with significant applications in engineering, physics, chemistry and most experimental fields.
In this volume, the authors emphasize the importance of problems associated with the construction of design. After a brief introduction on how the theory of optimal designs meets the theory of the uniform approximation of functions, the authors introduce the basic elements to design planning and link the statistical theory of optimal design and the theory of the uniform approximation of functions.
The appendices provide the reader with material to accompany the proofs discussed throughout the book.Elements from Approximation Theory. Uniform Approximation / Giorgio Celant, Michel Broniatowski
Convergence Rates for the Uniform Approximation and Algorithms / Giorgio Celant, Michel Broniatowski
Constrained Polynomial Approximation / Giorgio Celant, Michel Broniatowski
Optimal Designs for Polynomial Models. Interpolation and Extrapolation Designs for the Polynomial Regression / Giorgio Celant, Michel Broniatowski
An Introduction to Extrapolation Problems Based on Observations on a Collection of Intervals / Giorgio Celant, Michel Broniatowski
Instability of the Lagrange Interpolation Scheme With Respect to Measurement Errors / Giorgio Celant, Michel Broniatowski
Mathematical Material.
Appendix 1: Normed Linear Spaces-
Appendix 2: Chebyshev Polynomials
Appendix 3: Some Useful Inequalities for Polynomials