Interpolation and Extrapolation Optimal Designs V1 (eBook)

Giorgio Celant is Associate Professor in the Department of Statistical Sciences at the University of Padua in Italy. Michel Broniatowski is Full Professor in Theoretical and Applied Statistics at University Pierre and Marie Curie in Paris, France, and Vice-Chairman of the Statistics Department.

Chapter 1 - Approximation of continuous functions in normed spaces

Chapter 2 - Uniform approximation

Chapter 3 - Constrained polynomial approximation

Chapter 4 - Interpolation and extrapolation designs for the polynomial regression

Chapter 5 - Optimal extrapolation design for the Chebyshev regression

Chapter 6 - Optimal design for linear forms of the parameters in a Chebyshev regression

Chapter 7 -An introduction to extrapolation problems based on observations on a collection of intervals

Chapter 8 - Special topics and extensions

Chapter 9 - Instability of the Lagrange interpolation scheme with respect to measurement errors

"it seems that the book deserves more attention than a typical textbook, due to its particular features. Firstly, the authors are active researchers in the eld. Secondly, they concentrate mainly on characterizing optimal designs analytically. Both in the book and in their research, they put emphasis on optimal experiment design for function approximation or interpolation from observations with random errors"...."The book is rigorously written and it will be useful not only for advanced teaching, but also as a good starting point for further research" Ewaryst Rafaj lowicz, Mathematical Reviews, Sept 2017