### Abstract

Given a complex function w=f(z) defined in some region containing distinct points z_{1}, ..., z_{n}, we consider the divided difference table in the form of the divided difference matrix f^{+}(z_{1}, ..., z_{n}) whose (i, j) component equals f(z_{i}, ..., z_{j}) 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^{+}(z_{1}, ..., z_{n}), 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 z_{1}, ..., z_{n}.

Original language | English |
---|---|

Pages (from-to) | 404-405 |

Number of pages | 2 |

Journal | Journal of information processing |

Volume | 12 |

Issue number | 4 |

Publication status | Published - 1989 Dec 1 |

Externally published | Yes |

### ASJC Scopus subject areas

- Computer Science(all)

## Cite this

Ikebe, Y., Fujishiro, I., & Asayama, Y. (1989). Divided difference table from a matrix viewpoint.

*Journal of information processing*,*12*(4), 404-405.