On Modified Divided Differences II
نویسنده
چکیده
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 after the r¡a have been used. The perfect complementarity of the preceding m two sentences, together with the fact that £ Vudi can obviously be com0 puted starting with i = m as well as with i = 0, makes it clear that (6) may be computed using the information in the reverse order of that used in (8). Let Li denote the ordered set of 'words' of information
منابع مشابه
On 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...
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