منابع مشابه
A Note on Divided Differences
We obtain a new recurrence formula for sequences of divided differences. In a particular case, the recurrence formula simplifies the classical Newton–Girard identities relating power sums and elementary symmetric polynomials.
متن کاملOn Modified Divided Differences II
From (7) and (9) it is clear that the only essential information contained in Ei is the set of values i\u and the index rt. Note further that in (8), the successive Ei are used with increasing I and it follows from (9) that it is necessary to know ri before using the r¡n. On the other hand, in (6), the E¡ are used in decreasing sequence of / but from (7) it is not necessary to know rt until aft...
متن کاملOn Modified Divided Differences I
Although divided differences of a function are of basic importance in the theory of numerical analysis, they are not nearly as useful as ordinary differences in application. In the first place, they are much harder to generate ; not only because they involve unequal intervals of the argument, but because divisions are involved, often by small numbers. Furthermore, they are harder to interpret t...
متن کاملOn Modified Divided Differences I
Although divided differences of a function are of basic importance in the theory of numerical analysis, they are not nearly as useful as ordinary differences in application. In the first place, they are much harder to generate ; not only because they involve unequal intervals of the argument, but because divisions are involved, often by small numbers. Furthermore, they are harder to interpret t...
متن کاملDivided Differences
Starting with a novel definition of divided differences, this essay derives and discusses the basic properties of, and facts about, (univariate) divided differences. “It belongs to the most beautiful I have been able to do.”[Newton 1676]
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ژورنال
عنوان ژورنال: Publications de l'Institut Mathematique
سال: 2015
ISSN: 0350-1302,1820-7405
DOI: 10.2298/pim1512147g