Definition
We fix the interpolation nodes x0, …, xn and an interval containing all the interpolation nodes. The process of interpolation maps the function f to a polynomial p. This defines a mapping X from the space C of all continuous functions on to itself. The map X is linear and it is a projection on the subspace Πn of polynomials of degree n or less.
The Lebesgue constant Λn(T) is defined as the operator norm of X. This definition requires us to specify a norm on C. The maximum norm is usually the most convenient.
Read more about this topic: Lebesgue Constant (interpolation)
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