5. Approximation

Approximation theory is a fundamental part of numerical analysis. Many of the questions studied in the preceding paragraphs can be formulated within the framework of this theory: approximation of a function by an interpolating polynomial, of an integral by a finite sum, of the solution of a differential equation, etc.

We're going to give you the basics of approximation theory, which will require a minimum knowledge of functional analysis, but we won't go into the details, which can be studied in [19][31] . We'll focus more on examples to show the richness of this theory and the power of the tool provided by functional analysis. The first mathematician to draw attention to the potential contribution of functional analysis to the development of numerical...