Polynomial Approximation

Ionut Danaila (), Pascal Joly, Sidi Mahmoud Kaber and Marie Postel
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Ionut Danaila: Université de Rouen Normandie, CNRS, Laboratoire de mathématiques Raphaël Salem
Pascal Joly: Laboratoire Jacques-Louis Lions
Sidi Mahmoud Kaber: Sorbonne Université, CNRS, Université Paris Cité, Laboratoire Jacques-Louis Lions
Marie Postel: Sorbonne Université, CNRS, Université Paris Cité, Laboratoire Jacques-Louis Lions

Chapter Chapter 4 in An Introduction to Scientific Computing, 2023, pp 75-104 from Springer

Abstract: Abstract This project is devoted to the approximation of a given real function defined on an interval $$I=[a,b]\subset {\mathbb R}$$ I = [ a , b ] ⊂ R by a simpler one that belongs to the set $${\mathbb P}_n$$ P n the set $$x^k$$ x k of (algebraic) polynomials spanned by $$k=0,\cdots ,n$$ k = 0 , ⋯ , n ( $$n\in {\mathbb N}$$ n ∈ N ). Definitions and results of this chapter, given without proof, are widely used in the rest of the book.

Date: 2023
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DOI: 10.1007/978-3-031-35032-0_4

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