Divided difference table from a matrix viewpoint

Yasuhiko Ikebe, Issei Fujishiro, Yasusuke Asayama

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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.

Original languageEnglish
Pages (from-to)404-405
Number of pages2
JournalJournal of information processing
Issue number4
Publication statusPublished - 1989 Dec 1
Externally publishedYes

ASJC Scopus subject areas

  • General Computer Science

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