Given a complex function w=f(z) defined in some region containing distinct points z1, ..., zn, we consider the divided difference table in the form of the divided difference matrix f+(z1, ..., zn) whose (i, j) component equals f(zi, ..., zj) for i≤j and 0 elsewhere. Two theorems are proved: the first asserts that f→f+ is an algebraic homomorphism; the second gives a Cauchy contour-integral representation of f+(z1, ..., zn), which also equals the Cauchy formula for f(z+), where z+ denote the f+-matrix corresponding to f(z)=z and where f(z) is assumed analytic in a region containing z1, ..., zn.
|ジャーナル||Journal of information processing|
|出版ステータス||Published - 1989 12月 1|
ASJC Scopus subject areas
- コンピュータ サイエンス（全般）