In numerical mathematics, for the efficient evaluation of a
real-valued polynomial pn(x) the Horner's rule (HR) is employed
which is based on the identity
|
pn ( x ) | = a 0 x n + a 1
x n-1 + a 2 x n-2 + ... + a
n-2 x 2 + a n-1 x + a n |
| =((...(( a 0 x + a 1 ) x +
a 2 ) x + ... + a n-2 ) x + a n-1 ) x +
a n . |
|
|
7.1.
Explain, in how far this scheme constitutes an algorithm (compliance with the
intuitive notion of an algorithm, presence of all characteristic features of
an algorithm). Base your arguments on a representation of the HR using an
appropriate notation as e.g. structograms (cf. [1]),
decision tables, ... .
7.2.
Using the notation choosen previously, extend the algorithm HR to evaluate 
simultaneously with
pn(x).
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