The differential mean value of divided differences
نویسندگان
چکیده
منابع مشابه
Simplicial Differential Calculus, Divided Differences, and Construction of Weil Functors
We define a simplicial differential calculus by generalizing divided differences from the case of curves to the case of general maps, defined on general topological vector spaces, or even on modules over a topological ring K. This calculus has the advantage that the number of evaluation points grows linearly with the degree, and not exponentially as in the classical, “cubic” approach. In partic...
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]
متن کاملDivided differences of implicit functions
Divided differences can be viewed as a discrete analogue of derivatives and are commonly used in approximation theory, see [1] for a survey. Recently, the second author and Lyche established two univariate chain rules for divided differences [2], both of which can be viewed as analogous to Faà di Bruno’s formula for differentiating composite functions [6,7]. One of these formulas was simultaneo...
متن کاملBivariate mean value interpolation on circles of the same radius
We consider bivariate mean-value interpolationproblem, where the integrals over circles are interpolation data. In this case the problem is described over circles of the same radius and with centers are on astraight line and it is shown that in this case the interpolation is not correct.
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 کاملذخیره در منابع من
با ذخیره ی این منبع در منابع من، دسترسی به آن را برای استفاده های بعدی آسان تر کنید
ژورنال
عنوان ژورنال: Journal of Mathematical Analysis and Applications
سال: 2007
ISSN: 0022-247X
DOI: 10.1016/j.jmaa.2006.01.088