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Chapter 7. Convergence for Differentiable Functions by Lloyd Nicholas Trefethen is a book available to read on EtoBox.

What is Chapter 7. Convergence for Differentiable Functions about?

The principle mentioned at the end of the last chapter might be regarded as the central dogma of approximation theory: the smoother a function, the faster its approximants converge as n → ∞. Connections of this kind were explored in the early years of the 20th century by three of the founders of approximation theory: Charles de la Vallée Poussin (1866Poussin ( -1962)), a mathematician at Leuven in Belgium, Sergei Bernstein (1880-1968), a Ukrainian mathematician who had studied with Hilbert in Göttingen, and Dunham Jackson (1888-1946), an American student of Landau's also at Göttingen. (Henri Lebesgue in France (1875-1941) also proved some of the early results. For remarks on the history see [Goncharov 2000] and [Steffens 2006].) Bernstein made the following comment concerning best approximation errors E n (f ) = f − p \* n ∞ (see Chapter 10) in his summary article for the International Congress of Mathematicians in 1912 [Bernstein 1912a]:The general fact that emerges from this study is the existence of a most intimate connection between the differential properties of the function f (x) and the asymptotic rate of decrease of the positive numbersIn this and the next chapter our aim i

Author

Lloyd Nicholas Trefethen

Publisher

Society for Industrial and Applied Mathematics; SIAM - Society for Industrial and Applied Mathematics

Published

2019

Language

EN

ISBN

9781611975949

Subjects

Mathematics, Stem