It is well known, that any interpolating polynomial p(x, y) on the vector space Pn,m of two-variable polynomials with degree less than n in terms of x and less than m in terms of y, has various representations that depends on the basis of Pn,m that we select i.e. monomial, Newton and Lagrange basis e.t.c.. The aim of this short note is twofold : a) to present transformations between the coordinates of the polynomial p(x, y) in the aforementioned basis and b) to present transformations between these bases. Additionally, a computational numerical application that illustrate the usefulness of the transformations between two-variable polynomial bases is presented.
Digital Object Identifier (DOI)
Varsamis, Dimitris; Karampetakis, Nicholas; and Mastorocostas, Paris
"Transformations between Two-Variable Polynomial Bases with Applications,"
Applied Mathematics & Information Sciences: Vol. 10
, Article 9.
Available at: https://dc.naturalspublishing.com/amis/vol10/iss4/9