Interval Interpolation By Newtons Divided Differences
نویسندگان
چکیده
منابع مشابه
Lagrange Interpolation on a Lattice: Bounding Derivatives by Divided Differences
Fix an integer n > 0. For a multivariate function defined on a (not necessarily rectangular) lattice, an extension is constructed to have, ∀k ≤ n, derivatives of total degree k that are bounded by the function’s tensor product divided differences of total degree k times a constant independent of the lattice and the function. The extension is locally constructed, can have any prescribed smoothne...
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We present parallel algorithms for fast polynomial interpolation. These algorithms can be used for constructing and evaluating polynomials interpolating the function values and its derivatives of arbitrary order (Hermite interpolation). For interpolation, the parallel arithmetic complexity is 0(log2 M + log N) for large M and N, where M 1 is the order of the highest derivative information and N...
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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...
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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...
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ژورنال
عنوان ژورنال: Journal of Mathematics and Computer Science
سال: 2014
ISSN: 2008-949X
DOI: 10.22436/jmcs.013.03.05