In
mathematics, the Lebesgue constants (depending on a set of nodes and of its size) give an idea of how good the
interpolant
In the mathematical field of numerical analysis, interpolation is a type of estimation, a method of constructing (finding) new data points based on the range of a discrete set of known data points.
In engineering and science, one often has a ...
of a
function
Function or functionality may refer to:
Computing
* Function key, a type of key on computer keyboards
* Function model, a structured representation of processes in a system
* Function object or functor or functionoid, a concept of object-oriente ...
(at the given nodes) is in comparison with the best
polynomial
In mathematics, a polynomial is an expression consisting of indeterminates (also called variables) and coefficients, that involves only the operations of addition, subtraction, multiplication, and positive-integer powers of variables. An example ...
approximation of the function (the degree of the polynomials are fixed). The Lebesgue constant for polynomials of degree at most and for the set of nodes is generally denoted by . These constants are named after
Henri Lebesgue
Henri Léon Lebesgue (; June 28, 1875 – July 26, 1941) was a French mathematician known for his theory of integration, which was a generalization of the 17th-century concept of integration—summing the area between an axis and the curve of ...
.
Definition
We fix the interpolation nodes
and an
interval