منابع مشابه
On 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 کاملRecurrence Relations For Computing With Modified Divided Differences
Abstract. Modified divided differences (MDD) provide a good way of representing a polynomial passing through points with unequally spaced abscissas. This note gives recurrence relations for computing coefficients in either the monomial or Chebyshev basis from the MDD coefficients, and for computing the MDD coefficients for either the differentiated or the integrated polynomial. The latter opera...
متن کاملA 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.
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ژورنال
عنوان ژورنال: Mathematics of Computation
سال: 1954
ISSN: 0025-5718
DOI: 10.1090/s0025-5718-1954-0061883-0