In
mathematics
Mathematics is a field of study that discovers and organizes methods, Mathematical theory, theories and theorems that are developed and Mathematical proof, proved for the needs of empirical sciences and mathematics itself. There are many ar ...
, the Lebesgue constants (depending on a set of nodes and of its size) give an idea of how good the
interpolant of a
function (at the given nodes) is in comparison with the best
polynomial
In mathematics, a polynomial is a Expression (mathematics), mathematical expression consisting of indeterminate (variable), indeterminates (also called variable (mathematics), variables) and coefficients, that involves only the operations of addit ...
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.
Definition
We fix the interpolation nodes
and an
interval