Birkhoff interpolation

# Birkhoff interpolation

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Encyclopedia
In mathematics
Mathematics
Mathematics is the study of quantity, space, structure, and change. Mathematicians seek out patterns and formulate new conjectures. Mathematicians resolve the truth or falsity of conjectures by mathematical proofs, which are arguments sufficient to convince other mathematicians of their validity...

, Birkhoff interpolation is an extension of polynomial interpolation
Polynomial interpolation
In numerical analysis, polynomial interpolation is the interpolation of a given data set by a polynomial: given some points, find a polynomial which goes exactly through these points.- Applications :...

. It refers to the problem finding a polynomial p of degree d such that
where the data points and the nonnegative integers are given. It differs from Hermite interpolation
Hermite interpolation
In numerical analysis, Hermite interpolation, named after Charles Hermite, is a method of interpolating data points as a polynomial function. The generated Hermite polynomial is closely related to the Newton polynomial, in that both are derived from the calculation of divided differences.Unlike...

in that it is possible to specify derivatives of p at some points without specifying the lower derivatives or the polynomial itself. The name refers to George David Birkhoff
George David Birkhoff